By definition of composition of functions you know that
[tex](f\circ g)(x)=f(g(x))[/tex]So replacing g(x) into f(x) you have
[tex]\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}[/tex]Therefore,
[tex](f\circ g)(x)=x^2-6x+16[/tex]