Question

Se f(x) = 5x + 1 e h(x) = 1 + 4x, calcule f(h(2)) - h(f(2)) Alguém me ajuda?

Answer 1

Vamos começar determinando f(h(x)) e  h(f(x)):

$f(h(x))~=~5~.~(1+4x)~+~1\\\\\\f(h(x))~=~5+20x+1\\\\\\\boxed{f(h(x))~=~20x+6}\\\\\\\\h(f(x))~=~1~+~4~.~(5x+1)\\\\\\h(f(x))~=~1+20x+4\\\\\\\boxed{h(f(x))~=~20x+5}$

Agora podemos determinar a expressão:

$f(h(2))~-~h(f(2))~=~(20~.~2~+~6)~-~(20~.~2~+~5)\\\\\\f(h(2))~-~h(f(2))~=~(40+6)~-~(40+5)\\\\\\\boxed{f(h(2))~-~h(f(2))~=~1}$