Question

Dada as funções f ( x ) = x² + 2 x, encontre F ( f ( x ) ) (15 pontos )

Answer 1

$f(x)=x^2+2x\\\\f(f(x))=(x^2+2x)^2+2\cdot(x^2+2x)\\\\f(f(x))=x^4+4x^3+4x^2+2x^2+4x\\\\\boxed{f(f(x))=x^4+4x^3+6x^2+4x}$

Answer 2

F( x ) = x2 + 2x
F ( F(x) ) = ( F(x) )2 + 2( F(x) )
F (x2 +2x) = (x2+2x)2 + 2(x2+2x)

x4 + 4x3 + 4x2 + 2x2 + 4x
x4 + 4x3 +6x2 + 4x