Answer
$$f^{-1}(x)=\sqrt{x-4}$$
Work Step by Step
To find the inverse of $f(x)=y=x^2+4$, one must solve the equation for $x$. So we have$$y=x^2+4 \quad \Rightarrow \quad x^2=y-4 \quad \Rightarrow \quad x=\pm \sqrt{y-4}$$But since, by the assumption, $x \ge 0$, we get$$x=\sqrt{y-4}$$Thus, the inverse of the function is$$f^{-1}(x)=\sqrt{x-4}$$
