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Lista 2-Ca´lculo I-Equipe 3 Operac¸o˜es com func¸o˜es Func¸a˜o composta Transformac¸o˜es em gra´ficos 1. Se f(x) = 3x2 + 2 e g(x) = 1 3x+ 2 , determine: (a) (f + g)(x) (b) (f(x))−1 (c) (f · g)(x) (d) ( f g ) (x) (e) ( g f ) (x) (f) (f ◦ g)(x) 2. Seja f(x) = 3− x x . Determine: (a) f ( x2 )− (f(x))2 (b) f (1 x ) − 1 f(x) (c) (f ◦ f)(x) 3. Dadas f(x) = { −x , x < 0 x2 , x ≥ 0 e g(x) = { 1 x , x < 0√ x , x ≥ 0 , determine: (a) (f ◦ g)(x) (b) (g ◦ f)(x) Nos exerc´ıcios 4. a 11., a partir do gra´fico da func¸a˜o y = f(x) dado abaixo, esboce o gra´fico da func¸a˜o dada. 4. y = f (|x|) 5. y = |f(x)| 6. y = f(−x) 7. y = −f(x) 8. y = f(x+ 2) 9. y = f(x) + 3 10. y = f(x) + |f(x)| 2 11. y = f(x)− |f(x)| 2 x y = f(x) –4 –2 0 2 4 –8 –6 –4 –2 2 4 6 8 10 12 14 Esboce os gra´ficos das func¸o˜es dos exerc´ıcios 12. a 17. 12. f(x) = 8− 3√ x 2 − 1 13. f(x) = √ 2|x| − 6 14. f(x) = |x− 1|3 15. f(x) = 1 + 3 √ 1− x 16. f(x) = (|x| − 1)3 17. f(x) = ∣∣x2 − 4|x|+ 3∣∣ Nos exerc´ıcios 18. a 21. determime o domı´nio, a imagem e esboce o gra´fico da func¸a˜o dada. 18. f(x) = 3 sen (2pix) 19. f(x) = tan (x 2 ) 20. f(x) = ∣∣∣∣ sen (x2 ) − 1 2 ∣∣∣∣ , 0 ≤ x ≤ 4pi 21. f(x) = 1 2 sec ( x− pi 3 ) Lista 2-Ca´lculo I-Equipe 4 RESPOSTAS 1. (a) y = 9x3 + 6x2 + 6x+ 5 3x+ 2 , x 6= −2 3 (b) y = 1 3x2 + 2 (c) y = 3x2 + 2 3x+ 2 , x 6= −2 3 (d) y = 9x3 + 6x2 + 6x+ 4, x 6= −2 3 (e) y = 1 9x3 + 6x2 + 6x+ 4 , x 6= −2 3 (f) y = 18x2 + 24x+ 11 9x2 + 12x+ 4 , x 6= −2 3 2. (a) y = 6x− 2x2 − 6 x2 (b) y = 9x− 3x2 − 3 3− x (c) y = 4x− 3 3− x 3. (a) (f ◦ g)(x) = { − 1 x , x < 0 x , x ≥ 0 (b) (g ◦ f)(x) = { √−x , x < 0 x , x ≥ 0 4. y x –4 –2 2 4 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 5. y x –4 –2 2 4 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 6. y x –4 –2 2 4 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 7. y x –4 –2 2 4 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 8. y x –4 –2 2 4 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 9. y x –2 0 2 4 6 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 10. y x –4 –2 2 4 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 11. y x –4 –2 2 4 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 12. y x –2 2 4 6 8 10 20 13. y x 0 2 4 6 8 –10 –8 –6 –4 –2 2 4 6 8 10 14. x y 1 2 –2 2 4 15. y x –2 0 2 –4 –2 2 4 6 16. x y –1 1 2 –4 –3 –2 –1 1 2 3 4 17. y x 2 4 –6 –4 –2 2 4 6 18. y x –2 0 2 –6 –4 –2 2 4 6 19. y x –10 10 –10 10 20. x0 1 2 3 5 10 21. y x –10 –5 5 10 –15 –10 –5 5 10 15
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