Question

seja a função f (x+2) = x³ +3f(x) e f(1) = 3, calcule o valor de f(5)

Answer 1

Vamos começar determinando o valor de f(3) atribuindo o valor 1 para "x":

$f(x+2)~=~x^3+3f(x)\\\\\\Para~x=1\\\\\\f(1+2)~=~1^3~+~3f(1)\\\\\\f(3)~=~1+3\,.\,3\\\\\\f(3)~=~1+9\\\\\\\boxed{f(3)~=~10}$

Agora sim, atribuindo o valor 3 para "x", podemos determinar o valor de f(5):

$f(3+2)~=~3^3+3\,.\,f(3)\\\\\\f(5)~=~27+30\\\\\\\boxed{f(5)~=~57}$