Question

Given f(x)=x² +7 and g(x)=x-3, find (fog)(x)

Answer 1

By definition of composition of functions you know that

$(f\circ g)(x)=f(g(x))$

So replacing g(x) into f(x) you have

$\begin{gathered} f(x)=x^2+7 \\ (f\circ g)(x)=(x-3)^2+7 \\ (f\circ g)(x)=(x-3)(x-3)^{}+7 \\ (f\circ g)(x)=x^2-3x-3x+9+7 \\ (f\circ g)(x)=x^2-6x+16 \end{gathered}$

Therefore,

$(f\circ g)(x)=x^2-6x+16$