<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/63df546d-6390-483f-9947-b4f487219eb7/bg1.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsf ws14">MATEMÁTICA (<span class="ls10 ws0">61</span><span class="ws1">)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM </span></div><div class="t m0 x1 h2 y3 ff1 fs0 fc0 sc0 lsf ws14">RECUPERATORI<span class="blank _0"></span>O 1° PARCIAL </div><div class="t m0 x2 h2 y4 ff1 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h2 y5 ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h3 y6 ff2 fs1 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h2 y7 ff2 fs0 fc0 sc0 ls11 ws2">21<span class="lsf ws3">/06/2023<span class="ff1 ws14"> <span class="blank _0"></span> <span class="blank _1"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 1 </span></span></div><div class="t m0 x3 h2 y8 ff2 fs0 fc0 sc0 lsf ws14"> Hoja 1 de 4 </div><div class="t m0 x3 h2 y9 ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h3 ya ff2 fs1 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h3 yb ff2 fs1 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h4 yc ff3 fs2 fc0 sc0 lsf ws14">Tabla de uso exclusivo para el docente </div></div><div class="c x4 yd w3 h5"><div class="t m0 x5 h6 ye ff3 fs3 fc0 sc0 lsf ws14"> </div></div><div class="c x6 yd w4 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws14">1 </div></div><div class="c x8 yd w5 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws14">2 </div></div><div class="c x9 yd w6 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws14">3 </div></div><div class="c xa yd w7 h5"><div class="t m0 x7 h6 ye ff3 fs3 fc0 sc0 lsf ws14">4 </div></div><div class="c x4 yf w3 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws14"> </div></div><div class="c x6 yf w4 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws14"> </div></div><div class="c x8 yf w5 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws14"> </div></div><div class="c x9 yf w6 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws14"> </div></div><div class="c xa yf w7 h7"><div class="t m0 xb h8 y10 ff4 fs2 fc0 sc0 lsf ws14"> </div></div><div class="c x4 y11 w5 h9"><div class="t m0 xb ha y12 ff4 fs4 fc0 sc0 lsf ws14">Puntaje de cada </div><div class="t m0 xb ha y13 ff4 fs4 fc0 sc0 lsf ws14">ejercicio </div></div><div class="c x6 y11 w4 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws14">2,50 </div></div><div class="c x8 y11 w5 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws14">2,50 </div></div><div class="c x9 y11 w6 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws14">2,50 </div></div><div class="c xa y11 w7 h9"><div class="t m0 xc h8 y14 ff4 fs2 fc0 sc0 lsf ws14">2,50 </div></div><div class="c x0 y1 w2 h0"><div class="t m0 x1 hb y15 ff5 fs5 fc0 sc0 lsf ws14">Duración del exam<span class="blank _3"> </span>en: 1h <span class="ff6 ws4">40\u2019.</span> Com<span class="blank _3"> </span>pletar los datos<span class="blank _3"> </span> personales<span class="blank _3"> </span> con letra clara, m<span class="blank _3"> </span>ayúscula e imprenta. <span class="blank _3"> </span> </div><div class="t m0 xd hc y16 ff3 fs5 fc0 sc0 lsf ws14">No se aceptarán respue<span class="blank _3"> </span>stas en lápiz.<span class="blank _3"> </span> </div><div class="t m0 xe hd y17 ff2 fs6 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 he y18 ff7 fs2 fc0 sc0 lsf ws14">1. Hallar el valor de <span class="ff8 ws5">\uee89</span> para que la función <span class="ff8 ls0">\uee8c<span class="ls1 v1">\udb80\udddb</span><span class="ls2">\uee9e<span class="ls3 v1">\udb80\udddc</span><span class="ls4">\uf34c<span class="fs7 lsf v2">\uf0dd</span></span></span></span></div><div class="t m0 xf hf y19 ff8 fs7 fc0 sc0 ls5">\uee9e<span class="fs8 ls6 v3">\uf0db</span><span class="ls7">\uf13f<span class="ls12 ws6">\uf0da\uf0db\uee9e</span><span class="lsf ws7">\uf13e\uee89</span></span></div><div class="t m0 x9 h10 y18 ff7 fs2 fc0 sc0 lsf ws14"> tenga una asíntota en <span class="ff8 ws8">\uee9e\ue603<span class="blank"> </span>\uf34c<span class="blank"> </span>\ue603\uf0e1</span>. </div><div class="t m0 x10 h10 y1a ff9 fs2 fc0 sc0 lsf ws14">Si la recta <span class="ff8 ws9">\ued54<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\ue97a</span> es asíntota de la func<span class="blank _0"></span>ión significa que: </div><div class="t m0 x11 h10 y1b ff8 fs2 fc0 sc0 lsf ws5">\ued48\ued45\ued49</div><div class="t m0 x11 h11 y1c ff8 fs7 fc0 sc0 lsf wsa">\uf1eb\ueb5c\uf13c<span class="blank _5"> </span><span class="fs2 ls8 v4">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="lsa v1">\udb80\udddc</span><span class="lsf wsb">\uf34c<span class="blank _6"> </span>\ue9bb\ue603\ue603\ue603<span class="blank _6"> </span>\uf43a<span class="blank"> </span>\ue603\ue603\ue603<span class="blank"> </span>\ued48\ued45\ued49</span></span></span></div><div class="t m0 x12 h12 y1c ff8 fs7 fc0 sc0 lsf wsc">\uf1eb<span class="blank"> </span>\ueb5c\uf13c<span class="blank _5"> </span><span class="fs2 lsb v4">\ue603</span><span class="fs2 v5">\ue976</span></div><div class="t m0 x13 h13 y1d ff8 fs2 fc0 sc0 lsc">\ued54<span class="fs7 lsd v6">\uf136</span><span class="lse">\uf346<span class="ls13 wsd">\ue973\ue974</span><span class="lsf wse">\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _4"> </span><span class="ws8 v7">\uf34c<span class="blank"> </span>\ue9bb<span class="ffa ws14"> </span></span></span></span></div><div class="t m0 x10 h10 y1e ff9 fs2 fc0 sc0 lsf ws14">Como <span class="blank _8"> </span>el <span class="blank _8"> </span>numerador <span class="blank _8"> </span>es <span class="blank _8"> </span><span class="ff8 ws5">\ue976</span>, <span class="blank _8"> </span>para <span class="blank _8"> </span>que <span class="blank _8"> </span>esto <span class="blank _8"> </span>se<span class="blank _0"></span>a <span class="blank _8"> </span>posible <span class="blank _8"> </span>el <span class="blank _8"> </span>denominador <span class="blank _8"> </span>debe <span class="blank _8"> </span>aproximarse <span class="blank _8"> </span>a <span class="blank _8"> </span><span class="ff8 ws5">\ue972</span> <span class="blank _8"> </span>cuando <span class="blank _8"> </span><span class="ff8 ls9">\ued54</span> <span class="blank _8"> </span>se<span class="blank _3"> </span> </div><div class="t m0 x10 h10 y1f ff9 fs2 fc0 sc0 lsf ws14">aproxima a <span class="ff8 ws5">\ue97a</span>. </div><div class="t m0 x10 h14 y20 ff9 fs2 fc0 sc0 lsf ws14">Por lo tanto resolvemos la ecuación <span class="ff8 lsc">\ued54<span class="fs7 lsd v8">\uf136</span><span class="lse">\uf346<span class="ls13 wsd">\ue973\ue974<span class="lsf wsf">\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _4"> </span>\uf34c<span class="blank _6"> </span>\ue972</span></span></span></span> cuando <span class="ff8 ws8">\ued54<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\ue97a</span>. </div><div class="t m0 x14 h14 y21 ff8 fs2 fc0 sc0 lsf ws5">\ue97a<span class="fs7 lsd v8">\uf136</span><span class="lse">\uf346<span class="ls13 wsd">\ue973\ue974</span></span><span class="ws10">\ue7e4\ue97a<span class="blank"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _9"> </span>\uf34c<span class="blank _7"> </span>\ue972\ue603<span class="blank _6"> </span>\uf43a<span class="blank _6"> </span><span class="ls13 ws11">\ue978\ue976<span class="blank"> </span><span class="lse">\uf346</span><span class="ws12">\ue97b\ue978<span class="blank"> </span></span></span><span class="wse">\uf345<span class="blank"> </span>\ued3f<span class="blank _4"> </span>\uf34c<span class="blank _6"> </span>\ue972\ue603<span class="blank _7"> </span>\uf43a<span class="blank _6"> </span>\uf346<span class="ls13 ws11">\ue975\ue974<span class="blank"> </span></span><span class="ws13">\uf345<span class="blank _7"> </span>\ued3f<span class="blank"> </span>\uf34c<span class="blank _7"> </span>\ue972\ue603<span class="blank _7"> </span>\uf43a<span class="blank"> </span>\ued3f<span class="blank"> </span>\uf34c<span class="blank _7"> </span><span class="ls13 wsd">\ue975\ue974</span><span class="ff9 ws14"> </span></span></span></span></div><div class="t m0 x1 h15 y22 ff9 fs2 fc0 sc0 lsf ws14">En este ejercicio trabajamos con la definición de Asíntota Vertical. </div><div class="t m0 x1 h6 y23 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y24 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y25 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y26 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y27 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y28 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y29 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y2a ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y2b ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h6 y2c ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h16 y2d ff5 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h16 y2e ff5 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h16 y2f ff5 fs3 fc0 sc0 lsf ws14"> <span class="blank _a"> </span> </div></div><div class="c x1 y30 w8 h17"><div class="t m0 x15 h2 y31 ff2 fs0 fc0 sc0 lsf ws14">APELLIDO: </div></div><div class="c x16 y32 w9 h18"><div class="t m0 xb h2 y33 ff2 fs0 fc0 sc0 lsf ws14">CALIFICACIÓN:<span class="blank _0"></span> </div></div><div class="c x1 y34 w8 h19"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws14">NOMBRE: </div></div><div class="c x1 y32 w8 h19"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws14">DNI (registrado en S<span class="blank _0"></span>IU Guaraní): </div></div><div class="c x1 y35 w8 h1a"><div class="t m0 xb h2 y10 ff2 fs0 fc0 sc0 lsf ws14">E-MAIL: </div></div><div class="c x16 y36 w9 h1b"><div class="t m0 xb h2 y37 ff2 fs0 fc0 sc0 lsf ws14">DOCENTE (nombre<span class="blank _0"></span> y apellido): </div></div><div class="c x1 y38 w8 h19"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws14">TEL: </div></div><div class="c x1 y36 w8 h19"><div class="t m0 xb h2 y14 ff2 fs0 fc0 sc0 lsf ws14">AULA: </div></div><div class="c x0 y39 wa h1c"><div class="t m0 x15 h1d y3a ff4 fs3 fc1 sc0 lsf ws14"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y3b wb h1e" alt="" src="https://files.passeidireto.com/63df546d-6390-483f-9947-b4f487219eb7/bg2.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsf ws14">MATEMÁTICA (6<span class="ls10 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls14"> <span class="ls15"> </span></span>RECUPERATOR<span class="blank _3"> </span>IO 1° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 lsf ws14">APELLIDO Y NOMB<span class="blank _0"></span>RE: <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> DNI:<span class="ff1"> <span class="blank _b"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 1 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 lsf ws14">Hoja 2 de 4 </div><div class="t m0 x3 h2 y3c ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x2 h2 y3d ff1 fs0 fc0 sc0 ls16 ws14"> <span class="ff7 fs2 lsf v9">2. Hallar los valores de <span class="ff8 ws15">\uee89\ue603<span class="blank"> </span>\uebd0<span class="blank"> </span>\ueb39</span> para que la función <span class="ff8 ws16">\uee8c\udb80\udddb<span class="blank _3"> </span>\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank"> </span>\uf346<span class="blank _3"> </span>\uee9e<span class="fs7 ls17 v8">\uf0db</span><span class="lse ws17">\ue603<span class="blank _c"></span>\uf345\uee9e\uf345\uee89<span class="blank _d"></span><span class="ff7 lsf ws14"> se interseque con la función </span></span></span></span></div><div class="t m0 x1 h14 y3e ff8 fs2 fc0 sc0 lsf ws18">\uee8d\udb80\udddb\uee9e\udb80\udddc<span class="blank"> </span>\uf34c<span class="blank _6"> </span>\uee9e<span class="fs7 ls17 v8">\uf0db</span><span class="wse">\ue603<span class="blank _e"> </span>\uf345<span class="blank"> </span>\uee9e<span class="blank"> </span>\uf345<span class="blank"> </span>\uf0dc<span class="ff7 ws14">. </span></span></div><div class="t m0 x1 h16 y3f ff5 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h15 y40 ff9 fs2 fc0 sc0 lsf ws14">Para hallar los puntos en de intersección de las funciones de<span class="blank _0"></span>bemos plantear:<span class="blank _3"> </span> </div><div class="t m0 xf h1f y41 ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls18 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="lsa v1">\udb80\udddc</span><span class="lsf ws19">\uf34c<span class="blank _6"> </span>\ued43\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc<span class="ff9 ws14"> </span></span></span></div><div class="t m0 x1 h15 y42 ff9 fs2 fc0 sc0 lsf ws14">Luego, reemplazamos por las fórmulas de<span class="blank _0"></span> las <span class="blank _3"> </span>funciones dadas en el enunciado y resulta que: </div><div class="t m0 x17 h14 y43 ff8 fs2 fc0 sc0 lsf ws1a">\uf346\ued54<span class="blank"> </span><span class="fs7 ls19 v8">\uf136</span><span class="wse">\ue603<span class="blank _8"> </span>\uf345<span class="blank"> </span>\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ued3f<span class="blank _4"> </span>\uf34c<span class="blank _6"> </span>\ued54<span class="blank _f"> </span><span class="fs7 ls1a v8">\uf136</span>\ue603<span class="blank _8"> </span>\uf345<span class="blank"> </span>\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ue975<span class="ff9 ws14"> </span></span></div><div class="t m0 x1 h15 y44 ff9 fs2 fc0 sc0 lsf ws14">Despejamos y obtenemos que: <span class="blank _10"> </span><span class="ff8 ws1a va">\ue974\ued54<span class="blank"> </span><span class="fs7 ls1a v8">\uf136</span><span class="ws1b">\ue603<span class="blank"> </span>\uf345<span class="blank _5"> </span>\ue975<span class="blank _5"> </span>\uf346<span class="blank _5"> </span>\ued3f<span class="blank _4"> </span>\uf34c<span class="blank _6"> </span>\ue972</span></span><span class="va"> </span></div><div class="t m0 x1 h15 y45 ff9 fs2 fc0 sc0 lsf ws14">Aplicamos la fórmula resolvente: </div><div class="t m0 x18 h10 y46 ff8 fs2 fc0 sc0 lsf">\ued54</div><div class="t m0 x19 h20 y47 ff8 fs7 fc0 sc0 lsf ws1c">\uf135\ue7e1\uf136<span class="blank"> </span><span class="fs2 ls1b v3">\uf34c</span><span class="fs2 ws10 vb">\ue972<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ws5 v0">\uf3a5<span class="v0">\ue972</span></span></span><span class="lsd vc">\uf136</span><span class="fs2 wse vb">\uf346<span class="blank"> </span>\ue976\ue7e4\ue974\ue7e4<span class="blank _11"> </span>\udb80\udddb\ue975<span class="blank"> </span>\uf346<span class="blank"> </span>\ued3f<span class="blank _3"> </span>\udb80\udddc</span></div><div class="t m0 x1a h21 y48 ff8 fs2 fc0 sc0 ls1c">\ue976<span class="ffa lsf ws14 v7"> </span></div><div class="t m0 x1 h15 y49 ff9 fs2 fc0 sc0 lsf ws14">Como <span class="blank _5"> </span>las <span class="blank _5"> </span>funciones <span class="blank _12"> </span>deben <span class="blank _12"> </span>intersecarse <span class="blank _12"> </span>en <span class="blank _12"> </span>un <span class="blank _5"> </span>punto, <span class="blank _5"> </span>la <span class="blank _12"> </span>ecuación <span class="blank _12"> </span>debe <span class="blank"> </span>tene<span class="blank _0"></span>r <span class="blank _12"> </span>una <span class="blank _5"> </span>única <span class="blank _12"> </span>soluc<span class="blank _3"> </span>ión <span class="blank _5"> </span>por <span class="blank _5"> </span>lo <span class="blank _12"> </span>que </div><div class="t m0 x1 h10 y4a ff8 fs2 fc0 sc0 lsf ws1d">\uf346\ue976\ue7e4\ue974\ue7e4<span class="blank _11"> </span>\udb80\udddb\ue975<span class="blank _5"> </span>\uf346<span class="blank _5"> </span>\ued3f<span class="blank"> </span>\udb80\udddc<span class="ff9 ws14"> debe ser cero, es decir: <span class="blank _13"> </span></span><span class="ws1e va">\uf346\ue976\ue7e4\ue974\ue7e4<span class="blank"> </span></span><span class="ls1 vd">\udb80\udddb</span><span class="va">\ue975<span class="blank _5"> </span>\uf346<span class="blank _5"> </span>\ued3f<span class="blank"> </span></span><span class="ls1d vd">\udb80\udddc</span><span class="ws8 va">\uf34c<span class="blank"> </span>\ue972<span class="ff9 ws14"> </span></span></div><div class="t m0 x1 h10 y4b ff9 fs2 fc0 sc0 lsf ws14">Por lo tanto, para que este producto sea nulo <span class="ff8 ws1f">\ue975<span class="blank _12"> </span>\uf346<span class="blank _7"> </span>\ued3f<span class="blank"> </span></span> debe ser c<span class="blank _0"></span>ero, entonces: </div><div class="t m0 x1b h10 y4c ff8 fs2 fc0 sc0 lsf ws8">\ue975<span class="blank _5"> </span>\uf346<span class="blank _5"> </span>\ued3f<span class="blank _9"> </span>\uf34c<span class="blank"> </span>\ue972<span class="blank"> </span>\ueb5e<span class="blank"> </span>\ued3f<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\ue975<span class="ff9 ws14"> </span></div><div class="t m0 x1 h15 y4d ff9 fs2 fc0 sc0 lsf ws14">Al resolver el ejercicio utilizamos los conceptos de func<span class="blank _0"></span>ión cuadrática y de ecuaciones cuadráticas. </div><div class="t m0 x1 h15 y4e ff9 fs2 fc0 sc0 lsf ws14"> </div><div class="t m0 x10 h1d y4f ff4 fs3 fc0 sc0 lsf ws14"> <span class="blank _14"> </span> </div></div><div class="c x0 y39 wa h1c"><div class="t m0 x15 h1d y3a ff4 fs3 fc1 sc0 lsf ws14"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y50 wc h22" alt="" src="https://files.passeidireto.com/63df546d-6390-483f-9947-b4f487219eb7/bg3.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 lsf ws14">MATEMÁTICA (6<span class="ls10 ws0">1)</span><span class="ff2"> Cátedra A: NUÑEZ, MYRIAM</span><span class="ls14"> <span class="ls15"> </span></span>RECUPERATOR<span class="blank _3"> </span>IO 1° PARC<span class="blank _3"> </span>IAL </div><div class="t m0 x1 h2 y3 ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h2 y4 ff2 fs0 fc0 sc0 lsf ws14">APELLIDO Y NOMB<span class="blank _0"></span>RE: <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> DNI:<span class="ff1"> <span class="blank _b"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 1 </span></div><div class="t m0 x3 h2 y5 ff2 fs0 fc0 sc0 lsf ws14">Hoja 3 de 4 </div><div class="t m0 x3 h2 y3c ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h1d y51 ff4 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h1f y52 ff7 fs2 fc0 sc0 lsf ws14">3. Determinar los conjuntos <span class="ff8 ls1e">\uee6f<span class="fs7 ls1f v8">\uf13e</span></span> y <span class="ff8 ls2">\uee6f<span class="fs7 ls1f v8">\uf13f</span></span> de la función <span class="ff8 ls0">\uee8c<span class="ls18 v1">\udb80\udddb</span><span class="ls2">\uee9e<span class="ls3 v1">\udb80\udddc</span><span class="lsf wse">\uf34c<span class="blank _7"> </span>\udb80\udddb\uee9e<span class="blank"> </span>\uf345<span class="blank"> </span>\uf0da\udb80\udddc<span class="blank _3"> </span><span class="fs7 ls20 v8">\uf0dc</span><span class="ws1e">\ue7e4<span class="blank"> </span>\udb80\udddb\uee9e<span class="fs7 ls21 v8">\uf0db</span><span class="lse">\uf346<span class="ls2b ws20">\uf0db\uee9e<span class="blank"> </span></span></span></span>\uf345<span class="blank"> </span>\uf0dc\udb80\udddc</span></span></span>. </div><div class="t m0 x1 h16 y53 ff5 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x10 h15 y54 ff9 fs2 fc0 sc0 lsf ws14">Solución: </div><div class="t m0 x1 h15 y55 ff9 fs2 fc0 sc0 lsf ws14">Para <span class="blank _f"> </span>resolver <span class="blank _8"> </span>e<span class="blank _0"></span>sta <span class="blank _8"> </span>a<span class="blank _0"></span>ctividad <span class="blank _15"> </span>se <span class="blank _15"> </span>trabajarán <span class="blank _f"> </span>los <span class="blank _15"> </span>siguientes <span class="blank _15"> </span>contenidos <span class="blank _15"> </span>abordados <span class="blank _f"> </span>durant<span class="blank _3"> </span>e <span class="blank _f"> </span>el <span class="blank _15"> </span>cuatrimestre: <span class="blank _15"> </span>Números </div><div class="t m0 x1 h15 y56 ff9 fs2 fc0 sc0 lsf ws14">Reales- <span class="blank _0"></span>Ecuaciones e <span class="blank _0"></span>inecuaciones- intervalo- <span class="blank _0"></span>Funciones- F<span class="blank _0"></span>unciones cuadráticas- <span class="blank _0"></span>Funciones <span class="blank _0"></span>polinómicas -Estudio </div><div class="t m0 x1 h15 y57 ff9 fs2 fc0 sc0 lsf ws14">de una función. </div><div class="t m0 x1 h15 y58 ff9 fs2 fc0 sc0 lsf ws14">Se <span class="blank _3"> </span>denomina <span class="blank _3"> </span>conjunto <span class="blank _f"> </span>de <span class="blank _3"> </span>positividad <span class="blank _f"> </span>de <span class="blank _3"> </span>la <span class="blank _3"> </span>función <span class="blank _f"> </span>al <span class="blank _3"> </span>conjunto <span class="blank _f"> </span>de <span class="blank _3"> </span>valores <span class="blank _3"> </span>del <span class="blank _f"> </span>dominio <span class="blank _3"> </span>para <span class="blank _3"> </span>los <span class="blank _f"> </span>cuales <span class="blank _3"> </span>la <span class="blank _3"> </span>función </div><div class="t m0 x1 h15 y59 ff9 fs2 fc0 sc0 lsf ws14">es positiva, lo mismo sucede con el conjunto de neg<span class="blank _0"></span>atividad cuando la función es negativa. <span class="blank _3"> </span> </div><div class="t m0 x1 h15 y5a ff9 fs2 fc0 sc0 lsf ws14">Para determinar los conjuntos de positividad y negatividad de la func<span class="blank _0"></span>ión debemos analizar su comportamiento.<span class="blank _3"> </span> </div><div class="t m0 x1c h1f y5b ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="lsa v1">\udb80\udddc</span><span class="lsf ws21">\uf34c<span class="blank _6"> </span>\udb80\udddb\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls22 v8">\uf137</span><span class="ws1a">\ue7e4<span class="blank _11"> </span>\udb80\udddb\ued54<span class="blank"> </span><span class="fs7 ls23 v8">\uf136</span><span class="wse">\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ue975\udb80\udddc<span class="ff9 ws14"> </span></span></span></span></span></div><div class="t m0 x1d h15 y5c ff9 fs2 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h10 y5d ff9 fs2 fc0 sc0 lsf ws14">Utilizando la gráfica de la función, se puede observar que la única raíz de la misma es el punto <span class="ff8 ws22">\udb80\udddb\uf346\ue973\ue7e2<span class="blank"> </span>\ue972\udb80\udddc</span>, este </div><div class="t m0 x1 h15 y5e ff9 fs2 fc0 sc0 lsf ws14">valor se puede obtener de: </div><div class="t m0 x1e h14 y5f ff8 fs2 fc0 sc0 lsf wse">\ue972<span class="blank _7"> </span>\uf34c<span class="blank _6"> </span>\udb80\udddb<span class="blank _3"> </span>\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls22 v8">\uf137</span><span class="ws1a">\ue7e4<span class="blank _11"> </span>\udb80\udddb\ued54<span class="blank"> </span><span class="fs7 ls23 v8">\uf136</span></span>\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ue975\udb80\udddc<span class="ff9 ws14"> </span></div><div class="t m0 x1 h15 y60 ff9 fs2 fc0 sc0 lsf ws14">Debemos <span class="blank _0"></span>recordar <span class="blank _0"></span>que e<span class="blank _0"></span>l producto <span class="blank _0"></span>de <span class="blank _0"></span>dos expresiones <span class="blank _0"></span>sólo <span class="blank _0"></span>nos da<span class="blank _0"></span> ce<span class="blank _0"></span>ro c<span class="blank _0"></span>uando alguna <span class="blank _0"></span>de <span class="blank _0"></span>las e<span class="blank _0"></span>xpresiones lo <span class="blank _0"></span>es, por </div><div class="t m0 x1 h15 y61 ff9 fs2 fc0 sc0 lsf ws14">lo tanto: </div><div class="t m0 x1 h14 y62 ff8 fs2 fc0 sc0 lsf ws23">\udb80\udddb\ued54<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls24 v8">\uf137</span><span class="ws24">\uf34c<span class="blank _7"> </span>\ue972\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank _16"> </span>\uebe9<span class="blank"> </span>\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603<span class="blank"> </span>\ued54<span class="blank _f"> </span><span class="fs7 lsd v8">\uf136</span><span class="wse">\uf346<span class="blank"> </span>\ue974\ued54<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue975<span class="blank _6"> </span>\uf34c<span class="blank _6"> </span>\ue972\ue603\udb80\udddb\ued3d\ued4c\ued48\ued45\ued3f\ued3d\ued49\ued4b\ued4f<span class="blank _3"> </span>\ue603<span class="ls2c ws25">\ued48\ued3d<span class="blank _3"> </span></span><span class="ws26">\ue603\ued42\ue6d7\ued4e\ued49\ued51\ued48\ued3d\ue603\ued40\ued41<span class="blank _3"> </span>\ue603\ued48<span class="blank"> </span>\ued3d<span class="blank"> </span>\ue603\ued4e\ued41\ued3f\ued4b\ued48\ued52\ued41\ued4a\ued50\ued41\udb80\udddc<span class="ff9 ws14"> </span></span></span></span></div><div class="t m0 x1 h10 y63 ff8 fs2 fc0 sc0 lsf wse">\ued54<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue973<span class="blank _6"> </span>\uf34c<span class="blank _17"> </span><span class="ls2 v0">\ue9be</span>\ue972</div><div class="t m0 x1f h23 y64 ff8 fs8 fc0 sc0 ls25">\uf22f<span class="fs2 lsf ws8 ve">\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ued54<span class="blank _4"> </span>\uf34c<span class="blank"> </span><span class="ws27 vf">\uf346\udb80\udddb\uf346<span class="blank _3"> </span>\ue974\udb80\udddc<span class="blank"> </span>\uf347<span class="blank"> </span><span class="ls0 v0">\uf3a5</span><span class="ws5">\udb80\udddb\uf346\ue974\udb80\udddc<span class="fs7 ls26 v6">\uf136</span><span class="wse">\uf346<span class="blank"> </span>\ue976\ue7e4\ue973\ue7e4\ue975</span></span></span></span></div><div class="t m0 x1b h24 y65 ff8 fs2 fc0 sc0 lsf ws28">\ue974\ue7e4\ue973<span class="blank"> </span><span class="ff9 ws14 v7"> </span></div><div class="t m0 x1 h25 y66 ff8 fs2 fc0 sc0 lsf ws29">\ued54<span class="blank"> </span>\uf34c<span class="blank _6"> </span>\uf346\ue973\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ue603\ued54<span class="blank"> </span>\uf34c<span class="blank _6"> </span><span class="wse vf">\ue974<span class="blank"> </span>\uf347<span class="blank"> </span></span><span class="ls2 v10">\ue9be</span><span class="ws10 vf">\ue976<span class="blank"> </span>\uf346<span class="blank"> </span><span class="ls13 ws2a">\ue973\ue974<span class="blank"> </span><span class="lsf ws2b">\uf34c<span class="blank"> </span>\uf346\ue97a</span></span></span></div><div class="t m0 x20 h26 y67 ff8 fs2 fc0 sc0 ls27">\ue974<span class="ls28 v7">\uf34c</span><span class="lsf wse v11">\ue974<span class="blank"> </span>\uf347<span class="blank"> </span></span><span class="ls2 v5">\ue9be</span><span class="lsf ws5 v11">\uf346\ue97a</span></div><div class="t m0 x21 h13 y67 ff8 fs2 fc0 sc0 ls29">\ue974<span class="ls1b v7">\uf34c<span class="ls2d ws2c">\ued30\ued4b<span class="lsf ws5">\ue603<span class="blank _3"> </span>\ued50\ued45\ued41\ued4a\ued41\ue603<span class="ls2c ws25">\ued4e\ued3d</span><span class="ws2d">\ue6c0\ued3f\ued41<span class="blank"> </span>\ued4f\ue603\ued34<span class="blank"> </span><span class="ff9 ws14"> </span></span></span></span></span></div><div class="t m0 x1 h15 y68 ff9 fs2 fc0 sc0 lsf ws14">Ahora bien, para determinar el conjunto de positividad la única expresión con raíz real debe ser mayor a cero. </div><div class="t m0 x22 h14 y69 ff8 fs2 fc0 sc0 lsf wse">\udb80\udddb\ued54<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls24 v8">\uf137</span><span class="ws2e">\uf350<span class="blank"> </span>\ue972\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank"> </span>\ue603\ue603\ue603\ue603\ued54<span class="blank _4"> </span>\uf350<span class="blank"> </span>\uf346\ue973\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank _11"> </span>\ue603<span class="blank _e"> </span>\ued25<span class="blank _f"> </span><span class="fs7 ls2a v8">\uf13e</span><span class="ws2f">\uf34c<span class="blank _7"> </span>\udb80\udddb<span class="blank _3"> </span>\uf346\ue973\ue7e2<span class="blank"> </span>\uf345\ue9bb\udb80\udddc<span class="ff9 ws14"> </span></span></span></div><div class="t m0 x1 h15 y6a ff9 fs2 fc0 sc0 lsf ws14">Lo mismo sucede con el conjunto de negatividad la expresión debe ser menor a cero </div><div class="t m0 x22 h14 y6b ff8 fs2 fc0 sc0 lsf wse">\udb80\udddb\ued54<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue973\udb80\udddc<span class="fs7 ls24 v8">\uf137</span><span class="ws2e">\uf34f<span class="blank"> </span>\ue972\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank"> </span>\ue603\ue603\ue603\ue603\ued54<span class="blank _4"> </span>\uf34f<span class="blank"> </span>\uf346\ue973\ue603\ue603\ue603\ue603<span class="blank"> </span>\ueb5c<span class="blank _11"> </span>\ue603<span class="blank _e"> </span>\ued25<span class="blank _f"> </span><span class="fs7 ls2a v8">\uf13f</span><span class="ws22">\uf34c<span class="blank _7"> </span>\udb80\udddb<span class="blank _3"> </span>\uf346\ue9bb\ue7e2<span class="blank"> </span>\uf346\ue973\udb80\udddc<span class="ff9 ws14"> </span></span></span></div><div class="t m0 x10 h15 y6c ff9 fs2 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h16 y6d ff5 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h16 y6e ff5 fs3 fc0 sc0 lsf ws14"> <span class="blank _a"> </span> </div></div><div class="c x0 y39 wa h1c"><div class="t m0 x15 h1d y3a ff4 fs3 fc1 sc0 lsf ws14"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y6f wb h27" alt="" src="https://files.passeidireto.com/63df546d-6390-483f-9947-b4f487219eb7/bg4.png"><div class="c x0 y1 w2 h0"><div class="t m0 x1 h16 y70 ff5 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h2 y71 ff1 fs0 fc0 sc0 lsf ws14">MATEMÁTICA (6<span class="blank _0"></span><span class="ls10 ws0">1)<span class="ff2 lsf ws14"> Cátedra A: <span class="blank _0"></span>NUÑEZ, MYRIA<span class="blank _0"></span>M<span class="ff1"> RECUPE<span class="blank _0"></span>RATORIO 1° PARCIAL<span class="blank _0"></span> </span></span></span></div><div class="t m0 x1 h2 y72 ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h2 y73 ff2 fs0 fc0 sc0 lsf ws14">APELLIDO Y NOMB<span class="blank _0"></span>RE: <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> <span class="blank _0"></span> DNI:<span class="ff1"> <span class="blank _b"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span> <span class="blank _2"> </span>TEMA 1 </span></div><div class="t m0 x3 h2 y74 ff2 fs0 fc0 sc0 lsf ws14">Hoja 4 de 4 </div><div class="t m0 x3 h2 y75 ff2 fs0 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 he y76 ff7 fs2 fc0 sc0 lsf ws14">4. Hallar <span class="ff8 ws5">\uee8c<span class="fs7 ws30 v8">\uf13f\uf0da<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="ls2">\uee9e</span><span class="v1">\udb80\udddc</span></span> , <span class="ff8 ws15">\uee87<span class="blank"> </span>\uebd0<span class="blank"> </span>\ueb39</span>; s<span class="ff9 ls2b">i <span class="ff8 ls2e">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="lsa v1">\udb80\udddc</span><span class="ls1b">\uf34c<span class="fs7 lsf ws31 v2">\uf13a\uf1d4\uf13f\uf1eb</span></span></span></span></span></div><div class="t m0 xd h28 y77 ff8 fs7 fc0 sc0 lsf ws32">\uf13f\uf136<span class="blank"> </span><span class="ff9 fs2 ws14 v12"> , se cumple: <span class="ff8 ls2f">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="lsf ws26">\ue974\ued3d<span class="ls1d v1">\udb80\udddc</span><span class="ws33">\uf34c<span class="blank _6"> </span>\ued42<span class="blank"> </span></span></span></span></span><span class="ws34 v13">\uf13f\uf135<span class="blank"> </span></span><span class="fs2 ls1 v14">\udb80\udddb</span><span class="fs2 wse v12">\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue976<span class="ws5 v1">\udb80\udddc</span><span class="ff9 ws14"> </span></span></div><div class="t m0 x1 h15 y78 ff9 fs2 fc0 sc0 lsf ws14">Para la realización de este ejercicio, recomendamos ver apuntes de: Función inversa </div><div class="t m0 x1 h1f y79 ff9 fs2 fc0 sc0 lsf ws14">Para <span class="blank _f"> </span>hallar <span class="blank _15"> </span>la <span class="blank _15"> </span>función <span class="blank _15"> </span>in<span class="blank _3"> </span>versa <span class="blank _f"> </span>de <span class="blank _8"> </span><span class="ff8 ws19">\ued42<span class="blank"> </span>\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc</span>, <span class="blank _15"> </span>como <span class="blank _15"> </span>nos <span class="blank _15"> </span>dan <span class="blank _15"> </span>de <span class="blank _15"> </span>dato <span class="blank _15"> </span>que <span class="blank _8"> </span><span class="ff8 ls8">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="lsf ws26">\ue974\ued3d<span class="blank"> </span><span class="lsa v1">\udb80\udddc</span><span class="ws33">\uf34c<span class="blank _7"> </span>\ued42<span class="blank"> </span><span class="fs7 ws35 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="wse">\ued3d<span class="blank _7"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls1 v1">\udb80\udddc</span></span></span></span></span>, <span class="blank _15"> </span>basta <span class="blank _15"> </span>con <span class="blank _15"> </span>encontrar <span class="blank _15"> </span>la </div><div class="t m0 x1 h1f y7a ff9 fs2 fc0 sc0 lsf ws14">imagen de <span class="ff8 ws1d">\ued42<span class="blank"> </span>\udb80\udddb\ued54<span class="blank"> </span>\udb80\udddc</span>, ya que la misma será el dominio de <span class="ff8 ls30">\ued42<span class="fs7 lsf ws36 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="ls1 v1">\udb80\udddc</span><span class="lsf ws5">\ue7e4</span></span></span> </div><div class="t m0 x1 h10 y7b ff9 fs2 fc0 sc0 lsf ws14">Al <span class="blank _3"> </span>despejar <span class="blank _3"> </span>l<span class="blank _3"> </span>a <span class="blank _f"> </span><span class="ff8 ws5">\ue7f2\ued54\ue7f3</span> <span class="blank _3"> </span>de <span class="blank _f"> </span>la <span class="blank _3"> </span>función <span class="blank _f"> </span><span class="ff8 ls8">\ued42</span><span class="ffb">, <span class="blank _f"> </span>y <span class="blank _3"> </span>realizando <span class="blank _f"> </span>un <span class="blank _3"> </span>cambio <span class="blank _f"> </span>de <span class="blank _3"> </span>variables <span class="blank _f"> </span>(intercambiamos <span class="blank _3"> </span>a <span class="blank _3"> </span>cada <span class="blank _f"> </span>\u201cy\u201d <span class="blank _3"> </span>po<span class="blank _3"> </span>r <span class="blank _3"> </span>\u201cx\u201d <span class="blank _f"> </span>y <span class="blank _3"> </span>la </span></div><div class="t m0 x1 h15 y7c ffb fs2 fc0 sc0 lsf ws14">\u201cx\u201d por \u201cy\u201d), lograremos encontrar dicha función inversa<span class="ff9">: </span></div><div class="t m0 x23 h25 y7d ff8 fs2 fc0 sc0 lsf ws2b">\ued55<span class="blank"> </span>\uf34c<span class="blank"> </span><span class="wse vf">\ue978\ued3d<span class="blank _16"> </span>\uf346<span class="blank"> </span>\ued54</span></div><div class="t m0 x24 h24 y7e ff8 fs2 fc0 sc0 lsf ws37">\uf346\ue974<span class="blank"> </span><span class="ff9 ws14 v7"> </span></div><div class="t m0 x1b h10 y7f ff8 fs2 fc0 sc0 lsf ws38">\uf346\ue974\ued55<span class="blank _6"> </span>\uf34c<span class="blank _6"> </span>\ue978\ued3d<span class="blank _16"> </span>\uf346<span class="blank _5"> </span>\ued54<span class="blank"> </span><span class="ff9 ws14"> </span></div><div class="t m0 x25 h10 y80 ff8 fs2 fc0 sc0 lsf ws19">\uf346\ue974\ued55<span class="blank _16"> </span>\uf346<span class="blank _5"> </span>\ue978\ued3d<span class="blank _4"> </span>\uf34c<span class="blank _6"> </span>\uf346\ued54<span class="blank"> </span><span class="ff9 ws14"> </span></div><div class="t m0 x8 h10 y81 ff8 fs2 fc0 sc0 lsf ws26">\ued54<span class="blank _4"> </span>\uf34c<span class="blank _6"> </span>\ue974\ued55<span class="blank _16"> </span>\uf345<span class="blank _5"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws14"> </span></div><div class="t m0 x1 h15 y82 ff9 fs2 fc0 sc0 lsf ws14">Realizando el cambio de variables que mencionamos anteriormente, nos quedará<span class="blank _0"></span>:<span class="blank _3"> </span> </div><div class="t m0 x26 h10 y83 ff8 fs2 fc0 sc0 lsf ws26">\ued55<span class="blank _6"> </span>\uf34c<span class="blank _6"> </span>\ue974\ued54<span class="blank _7"> </span>\uf345<span class="blank _5"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws14"> </span></div><div class="t m0 x1 h15 y84 ff9 fs2 fc0 sc0 lsf ws14">Es decir que, la función inversa es: </div><div class="t m0 x27 h1f y85 ff8 fs2 fc0 sc0 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="ls31 v1">\udb80\udddc</span><span class="lsf ws2d">\uf34c<span class="blank _6"> </span>\ue974\ued54<span class="blank _16"> </span>\uf345<span class="blank _5"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws14"> </span></span></span></div><div class="t m0 x1 h1f y86 ff9 fs2 fc0 sc0 lsf ws14">Como <span class="blank _8"> </span>sabemos <span class="blank _e"> </span>que <span class="blank _11"> </span><span class="ff8 ls8">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="lsf ws26">\ue974\ued3d<span class="lsa v1">\udb80\udddc</span><span class="ws33">\uf34c<span class="blank _6"> </span>\ued42<span class="blank"> </span><span class="fs7 ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="wse">\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue976<span class="ws5 v1">\udb80\udddc</span></span></span></span></span>, <span class="blank _e"> </span>si <span class="blank _8"> </span>evaluamos <span class="blank _e"> </span>en <span class="blank _e"> </span>cada <span class="blank _e"> </span>miembro <span class="blank _e"> </span>de <span class="blank _e"> </span>la <span class="blank _e"> </span>igualdad <span class="blank _11"> </span>y<span class="blank _0"></span> <span class="blank _8"> </span>luego <span class="blank _e"> </span>despejamos, </div><div class="t m0 x1 h10 y87 ffb fs2 fc0 sc0 lsf ws14">podremos obtener \u201c<span class="ff8 ls32">\ued3d</span>\u201d y por lo tanto la función inversa pedida:<span class="ff9"> </span></div><div class="t m0 x28 h1f y88 ff8 fs2 fc0 sc0 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="lsf wse">\ued3d<span class="blank"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls1d v1">\udb80\udddc</span><span class="ws1e">\uf34c<span class="blank _6"> </span>\ue603\ue974\ue7e4<span class="blank"> </span><span class="ls1 v1">\udb80\udddb</span></span>\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls33 v1">\udb80\udddc</span><span class="ws2d">\uf345<span class="blank _5"> </span>\ue978\ued3d<span class="blank"> </span><span class="ff9 ws14"> </span></span></span></div><div class="t m0 x29 h1f y89 ff8 fs2 fc0 sc0 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="lsf ws21">\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue976<span class="ls34 v1">\udb80\udddc</span><span class="wse">\uf34c<span class="blank _6"> </span>\ue974\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue97a<span class="blank"> </span>\uf345<span class="blank"> </span>\ue978\ued3d<span class="blank _3"> </span><span class="ff9 ws14"> </span></span></span></div><div class="t m0 x2a h1f y8a ff8 fs2 fc0 sc0 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="lsf wsf">\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue976<span class="lsa v1">\udb80\udddc</span><span class="wse">\uf34c<span class="blank _6"> </span>\ue97a\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue97a<span class="ff9 ws14"> </span></span></span></div></div><div class="c x0 y8b wa h29"><div class="t m0 x15 h1d y3a ff4 fs3 fc1 sc0 lsf ws14"><span class="fc2 sc0"> </span></div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x27 y8c wd h2a" alt="" src="https://files.passeidireto.com/63df546d-6390-483f-9947-b4f487219eb7/bg5.png"><div class="c x0 y1 w2 h0"><div class="t m0 x2b h15 y8d ff9 fs2 fc0 sc0 lsf ws14"> </div><div class="t m0 x1b h25 y8e ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="ls31 v1">\udb80\udddc</span><span class="ls28">\uf34c<span class="lsf wse vf">\ue978\ued3d<span class="blank _16"> </span>\uf346<span class="blank"> </span>\ued54</span></span></span></div><div class="t m0 x2c h24 y8f ff8 fs2 fc0 sc0 lsf ws39">\uf346\ue974<span class="blank"> </span><span class="ff9 ws14 v7"> </span></div><div class="t m0 x20 h25 y90 ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="lsf ws26">\ue974\ued3d<span class="ls31 v1">\udb80\udddc</span><span class="ls28">\uf34c</span><span class="wse vf">\ue978\ued3d<span class="blank _7"> </span>\uf346<span class="blank"> </span>\ue974\ued3d</span></span></div><div class="t m0 x2d h24 y32 ff8 fs2 fc0 sc0 lsf ws3a">\uf346\ue974<span class="blank"> </span><span class="ff9 ws14 v7"> </span></div><div class="t m0 x2e h25 y91 ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="lsf ws3b">\ue974\ued3d<span class="lsa v1">\udb80\udddc</span><span class="ls35">\uf34c</span><span class="ws5 vf">\ue976\ued3d</span></span></div><div class="t m0 x2d h24 y92 ff8 fs2 fc0 sc0 lsf ws5">\uf346\ue974<span class="ff9 ws14 v7"> </span></div><div class="t m0 x2f h1f y93 ff8 fs2 fc0 sc0 ls8">\ued42<span class="ls1 v1">\udb80\udddb</span><span class="lsf ws3b">\ue974\ued3d<span class="lsa v1">\udb80\udddc</span><span class="ws2d">\uf34c<span class="blank _6"> </span>\uf346\ue974\ued3d<span class="blank"> </span><span class="ff9 ws14"> </span></span></span></div><div class="t m0 x2b h15 y94 ff9 fs2 fc0 sc0 lsf ws14">Es decir que: </div><div class="t m0 x30 h1f y95 ff8 fs2 fc0 sc0 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="lsf wse">\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue976<span class="lsa v1">\udb80\udddc</span><span class="ws3b">\uf34c<span class="blank _6"> </span>\ued42<span class="blank"> </span>\udb80\udddb\ue974\ued3d<span class="blank"> </span>\udb80\udddc<span class="ff9 ws14">, entonces </span><span class="ws2d">\ue97a\ued3d<span class="blank _16"> </span>\uf345<span class="blank _16"> </span>\ue97a<span class="blank _6"> </span>\uf34c<span class="blank _7"> </span>\uf346\ue974\ued3d<span class="blank"> </span><span class="ff9 ws14"> </span></span></span></span></div><div class="t m0 x1b h10 y96 ff8 fs2 fc0 sc0 lsf wsf">\ue97a\ued3d<span class="blank _16"> </span>\uf345<span class="blank"> </span>\ue974\ued3d<span class="blank _4"> </span>\uf34c<span class="blank _7"> </span>\uf346\ue97a<span class="blank _3"> </span><span class="ff9 ws14"> </span></div><div class="t m0 x31 h10 y97 ff8 fs2 fc0 sc0 ls13 wsd">\ue973\ue972<span class="lsf ws9">\ued3d<span class="blank _4"> </span>\uf34c<span class="blank"> </span>\uf346\ue97a<span class="ff9 ws14"> </span></span></div><div class="t m0 x32 h25 y98 ff8 fs2 fc0 sc0 lsf ws3c">\ued3d<span class="blank _6"> </span>\uf34c<span class="blank"> </span>\uf346<span class="blank _18"> </span><span class="vf">\ue97a</span></div><div class="t m0 x13 h24 y99 ff8 fs2 fc0 sc0 ls13 wsd">\ue973\ue972<span class="ff9 lsf ws14 v7"> </span></div><div class="t m0 x33 h25 y9a ff8 fs2 fc0 sc0 lsf ws3d">\ued3d<span class="blank _6"> </span>\uf34c<span class="blank _6"> </span>\uf346<span class="blank"> </span><span class="vf">\ue976</span></div><div class="t m0 x34 h24 y9b ff8 fs2 fc0 sc0 ls36">\ue977<span class="ff9 lsf ws14 v7"> </span></div><div class="t m0 x1 h1f y9c ff9 fs2 fc0 sc0 lsf ws14">Reemplazando en <span class="ff8 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="ls3 v1">\udb80\udddc</span><span class="lsf ws2d">\uf34c<span class="blank _6"> </span>\ue974\ued54<span class="blank _7"> </span>\uf345<span class="blank _5"> </span>\ue978\ued3d<span class="blank"> </span></span></span></span>, resultará: </div><div class="t m0 x35 h25 y9d ff8 fs2 fc0 sc0 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="lsa v1">\udb80\udddc</span><span class="lsf ws3d">\uf34c<span class="blank _7"> </span>\ue974\ued54<span class="blank _7"> </span>\uf345<span class="blank _16"> </span>\ue978\ue7e4<span class="blank"> </span>\uf36c\uf346<span class="blank"> </span><span class="vf">\ue976</span></span></span></div><div class="t m0 x36 h13 y9e ff8 fs2 fc0 sc0 ls36">\ue977<span class="lsf ws5 v7">\uf370<span class="ff9 ws14"> </span></span></div><div class="t m0 x27 h2b y9f ff8 fs2 fc0 sc0 ls30">\ued42<span class="fs7 lsf ws34 v8">\uf13f\uf135<span class="blank"> </span></span><span class="ls1 v1">\udb80\udddb</span><span class="ls9">\ued54<span class="ls31 v1">\udb80\udddc</span><span class="lsf wse">\uf34c<span class="blank _7"> </span>\ue974\ued54<span class="blank _7"> </span>\uf346<span class="blank"> </span><span class="ls13 vf">\ue974\ue976</span></span></span></div><div class="t m0 x37 h24 ya0 ff8 fs2 fc0 sc0 ls37">\ue977<span class="ff9 lsf ws14 v7"> </span></div><div class="t m0 x1 h6 ya1 ff3 fs3 fc0 sc0 lsf ws14"> </div><div class="t m0 x1 h16 ya2 ff5 fs3 fc0 sc0 lsf ws14"> </div></div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div>
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