### Home > CCA2 > Chapter Ch10 > Lesson 10.3.1 > Problem10-161

10-161.

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

1. Sketch the graph and the inverse.

If you are stuck trying to sketch the graph, make a table.
Remember that to get an inverse, interchange the $x$- and $y$-values.

2. Find the equation of the inverse function.

Solve for: $y\text{: } x=\frac{\sqrt{y+4}}{2}-1$

3. Determine the domain and range of the inverse.

Look at your graphs in part (a).
What are the smallest and largest possible values of $x$?
What are the smallest and largest possible values of $y$?

4. Compute $f^{ -1}(f(5))$.

$5$