Question

sejam as funções f(x)=x²-7x+4 e g(x)=4x+3
a) (fog) (x)=

Answer 1

Para determinar a composta fog(x), vamos substituir a variável "x" de f(x) pela função g(x).

$fog(x)~=~f(g(x))\\\\\\fog(x)~=~\left(\,g(x)\,\right)^2-7\,.\,g(x)+4\\\\\\fog(x)~=~(4x+3)^2-7\,.\,(4x+3)+4\\\\\\fog(x)~=~(4x+3)\,.\,(4x+3)-(28x+21)+4\\\\\\fog(x)~=~(16x^2+12x+12x+9)-28x-21+4\\\\\\fog(x)~=~16x^2+24x+9-28x-17\\\\\\\boxed{fog(x)~=~16x^2-4x-8}$