EP2. Sean las funciones f(x) = x e g(x) = √(x^2 + 4x - 5). Determinar: (f ο g)(x), (g ο f)(x), (f ο h)(x), (h ο h)(x) a) (f ο g)(x) = √(x^2 + 4x ...
EP2. Sean las funciones f(x) = x e g(x) = √(x^2 + 4x - 5). Determinar: (f ο g)(x), (g ο f)(x), (f ο h)(x), (h ο h)(x)
a) (f ο g)(x) = √(x^2 + 4x - 5), (g ο f)(x) = √(x + 1), (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(2x^2)
b) (f ο g)(x) = √(x^2 + 4x - 5), (g ο f)(x) = x, (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(2x^2)
c) (f ο g)(x) = x, (g ο f)(x) = √(x + 1), (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(x^4)
d) (f ο g)(x) = x, (g ο f)(x) = x, (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(x^4)
a) (f ο g)(x) = √(x^2 + 4x - 5), (g ο f)(x) = √(x + 1), (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(2x^2)
b) (f ο g)(x) = √(x^2 + 4x - 5), (g ο f)(x) = x, (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(2x^2)
c) (f ο g)(x) = x, (g ο f)(x) = √(x + 1), (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(x^4)
d) (f ο g)(x) = x, (g ο f)(x) = x, (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(x^4)
💡 1 Resposta
Ed 
Para determinar as composições das funções, vamos substituir os valores de x nas expressões e simplificar: (f ο g)(x) = f(g(x)) = f(√(x^2 + 4x - 5)) = √(x^2 + 4x - 5) (g ο f)(x) = g(f(x)) = g(x) = √(x^2 + 4x - 5) (f ο h)(x) = f(h(x)) = f(e^(x^2)) = e^(x^2) (h ο h)(x) = h(h(x)) = h(e^(x^2)) = e^(2x^2) Portanto, a alternativa correta é: a) (f ο g)(x) = √(x^2 + 4x - 5), (g ο f)(x) = √(x^2 + 4x - 5), (f ο h)(x) = e^(x^2), (h ο h)(x) = e^(2x^2)
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