as you already know to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
[tex]\bf y=x^2+16\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\underline{y}^2+16}\implies x-16=y^2\implies \sqrt{x-16}=\stackrel{f^{-1}(x)}{y}[/tex]