Consider the function $f(x)=2+\sqrt{2x-4}$.

1. State the domain and range.

   Hint (a):

   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?

2. Write the equation of the inverse.

   Answer (b):

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

3. State the domain and range of the inverse function.

   Hint (c):

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