Chapter 2, Functions - Section 2.8 - One-to-One Functions and their Inverses - 2.8 Exercises - Page 262: 16

$g(x)$ is not one-to-one.

The function $g(x)=|x|$ is not one-to-one because it fails the horizontal line test (the graph has a V-shape). We can show that it has the same $y$ value for two different $x$ values: $g(1)=|1|=1$ $g(-1)=|-1|=1$ Thus the function is not one-to-one.