Question

Eu preciso do Gof e do Fog dessa função, por favor

Answer 1

Para a GoF, a função f(x) será a variável da função g, logo:

$\\g(f(x))~=~(f(x))^2~-3\\\\\\g(f(x))~=~(3x+2)^2-3\\\\\\g(f(x))~=~(3x+2)~.~(3x+2)~-~3\\\\\\g(f(x))~=~3x~.~3x~+~3x~.~2~+~2~.~3x~+~3~.~3~-~3\\\\\\g(f(x))~=~9x^2~+~6x~+~6x~+~9~-~3\\\\\\\boxed{g(f(x))~=~9x^2~+~12x~+~6}$

Para a FoG, a função g(x) será a variável da função f, logo:

$\\f(g(x))~=~3.(g(x))~+~2\\\\\\f(g(x))~=~3.(x^2~-~3)~+~2\\\\\\f(g(x))~=~3~.~x^2~-~3~.~3~+~2\\\\\\f(g(x))~=~3x^2~-~9~+~2\\\\\\\boxed{f(g(x))~=~3x^2~-~7}$