Question

dadas as funções f(x) = 2x e g (x) = x³, calcule:
a) g (f(1))
b) g (f(10))
c) f (g(1))
d) f (g(10))​

Answer 1

Vamos começar determinando as compostas gof e fog.

gof:

Para determinar a gof, tratamos a função f(x) como variável da função g.

$g(f(x))~=~(\,f(x)\,)^3\\\\\\g(f(x))~=~(2x)^3\\\\\\g(f(x))~=~2^3.x^3\\\\\\\boxed{g(f(x))~=~8x^3}$

fog:

Para determinar a fog, tratamos a função g(x) como variável da função f.

$f(g(x))~=~2\,.\,(\,g(x)\,)\\\\\\f(g(x))~=~2\,.\,(x^3)\\\\\\\boxed{f(g(x))~=~2x^3}$

a)

$g(f(1))~=~8\,.\,(1)^3\\\\\\g(f(1))~=~8\,.\,1\\\\\\\boxed{g(f(1))~=~8}$

b)

$g(f(10))~=~8\,.\,(10)^3\\\\\\g(f(10))~=~8\,.\,1000\\\\\\\boxed{g(f(10))~=~8000}$

c)

$f(g(1))~=~2\,.\,(1)^3\\\\\\f(g(1))~=~2\,.\,1\\\\\\\boxed{f(g(1))~=~2}$

d)

$f(g(10))~=~2\,.\,(10)^3\\\\\\f(g(10))~=~2\,.\,1000\\\\\\\boxed{f(g(10))~=~2000}$