Determine the inverse functions below.

1. If $f(x) = 2x - 3$, then what does $f^{ -1}(x)$ equal?

   Step 1(a):

   $f(x) + 3 = 2x$

   Step 2(a):

   $x=\frac{f(x)+3}{2}$

   Answer (a):

   $f^{-1}(x)=\frac{x+3}{2}$

2. If $h(x) = (x - 3)^2 + 2$, then what does $h^{-1}(x)$ equal?

   Hint (b):

   Follow the same steps as in part (a).

   Answer (b):

   $h^{-1}(x)=\sqrt{x-2}+3$

3. What is the domain of $h(x)$ from part (b) if both $h(x)$ and $h^{-1}(x)$ are functions?

   Answer (c):

   $x ≥ 3$