ANSWER
[tex]\begin{gathered} f(g(x))=x^{2}+9+8 \\ g(f(x))=x+16\sqrt{x}+73 \end{gathered}[/tex]EXPLANATION
Given;
[tex]f\left(x\right)=\sqrt{x}+8,\:g\left(x\right)=x^2+9[/tex][tex]f(g(x))[/tex]By substitution;
[tex]\begin{gathered} g(x)=x^2+9 \\ f(x^2+9)=\sqrt{x^2+9}+8 \\ f(g(x))=\sqrt{x^2+9}+8 \end{gathered}[/tex]For g(f(x));
By substitution;
[tex]\begin{gathered} \:g=x^2+9 \\ g(f(x))=\left(\sqrt{x}+8\right)^2+9 \end{gathered}[/tex]Solving the equation;
[tex]\begin{gathered} \begin{equation*} \left(\sqrt{x}+8\right)^2+9 \end{equation*} \\ =\left(\sqrt{x}\right)^2+2\sqrt{x}\cdot\:8+8^2+9 \\ =x+16\sqrt{x}+64+9 \\ =x+16\sqrt{x}+73 \end{gathered}[/tex]