For the function$f ( x ) = \frac { \sqrt { x + 4 } } { 2 } - 1$, complete parts (a) through (d) below.

1. Sketch the graph and the inverse.

   Hint (a):

   First, graph the function. Then, reflect the graph across
   y = x.

   Answer (a):

   

2. Find the equation of the inverse function.

   Hint (b):

   Replace f(x) with y, then switch the variables.

   $x=\frac{\sqrt{y+4}}{2}-1$

   Now solve for y.

   More Help (b):

   Do not forget to replace y with $f^{ − 1}\left(x\right)$.

   Answer (b):

   $f^{ −1}\left(x\right) = \left(2\left(x + 1\right)\right)^{2} − 4$

3. Determine the domain and range of the inverse.

   Hint (c):

   See graph in part (a).

   Answer (c):

   $x ≥ −1, y ≥ −4$

4. Compute $f ^{−1}\left(f \left(5\right)\right)$.

   Hint (d):

   Substitute $5$ for $x$ in the function $f\left(x\right)$. Now substitute the answer you found for $f\left(x\right)$ for $x$ in the inverse function
   f ⁻¹(x).

   Answer (d):

   $f^{ −1}\left(f\left(5\right)\right) = 5$