Question

16- Se f(x)=3x-5, g(x)=x2+2x-3, obter (fog)(2), (gof)(-3), (gof)(x) e (fog)(x).​

Answer 1

Resposta:

(gof)(x) = 9x² - 24x + 12

(gof)(-3) = 165

(fog)(x) = 3x² + 6x - 14

(fog)(2) = 10

Explicação passo-a-passo:

Para (gof)(x), obtemos:

$(gof)(x) = g(f(x)) = (3x-5)^2 +2(3x-5) - 3 = (9x^2 -30x+25)+(6x-10)-3 \Rightarrow\\\Rightarrow (gof)(x) = 9x^2-24x+12$

Substituindo x = -3:

$(gof)(-3) = 9(-3)^2-24(-3)+12 = 81+72+12 \Rightarrow\\\Rightarrow (gof)(-3) = 165$

Para (fog)(x), obtemos:

$(fog)(x) = 3(x^2+2x-3) - 5 = 3x^2+6x-9-5 \Rightarrow\\\Rightarrow (fog)(x) = 3x^2+6x-14$

Substituindo x = 2:

$(fog)(2) = 3(2)^2+6(2)-14 = 12 + 12 - 14 \Rightarrow\\\Rightarrow (fog)(2) = 10$