Given the function $f ( x ) = 2 + \sqrt { 2 x - 4 }$, find each of the following.

1. 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. The inverse equation.

   Answer (b):

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

3. The domain and range of the inverse.

   Hint (c):

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