Sketch a graph. What is the smallest $x$-value you can use before the number under the radical sign becomes negative?
What is the smallest $y$-value that can result from this equation?

$f^{-1}(x)=\frac{(x-2)^2}{2}+2$

Remember that in an inverse, $x$ and $y$ are interchanged. Reverse the domain and range you found in part (a).