### Home > PC > Chapter 3 > Lesson 3.2.1 > Problem3-58

3-58.

James is trying to find the inverse of $y=|x|$. Audrey says it is $x=|y|$.

1. Is Audrey correct? Explain briefly.

Yes. Switch $x$ and $y$.

2. Explain why the inverse of $y = x$ is not a function.

There is more than one possible output for each input.

3. How is the graph of $y = x$ related to the graph of its inverse $x=|y|$?

The graph of $y = \left|x\right|$ is the reflection of $x = \left|y\right|$ over the line $y = x$.

4. Write the function $y = x$ as a piecewise function by considering its graph, which consists of two rays.

$y = |x| = \begin{cases}x\text{ for }x \geq 0\\\:\:\:\:\:???\end{cases}$