Question

Sejam as funções f(x) = 2x + 5 e f(g(x)) = 6x + 1. Assim, g(– 2) é igual a
A) – 8
B) 6
C) 4
D) – 6
E) – 11

(Gabarito A , gostaria do passo a passo)

Answer 1

$Ola'! \\ \\ f(x)=2x+5~~~~~~~~~~~f\big(g(x)\big)=6x+1~~~~calulemos~\boxed{g(-2)=?} \\ \\ entao: \\ \underbrace{{ {f\big(g(x)\big)}}}_{6x+1}=2g(x)+5 \\ \\6x+1=2g(x)+5 \\ \\ 6x+1-5=2g(x) \\ \\ 2g(x)=6x-4 \\ \\ g(x)= \frac{6x-4}{2} \\ \\ g(x)=3x-2~~~sabemos~que~[x=-2] \\ \\ g(-2)=3(-2)-2 \\ \\\boxed{\boxed{ g(-2)=-8}}$