## College Algebra 7th Edition

The function $g(x)=\sqrt{x}$ is one-to-one because it passes the horizontal line test. We can show this algebraically: We start with the assumption that: $x_1\ne x_2$ Then: $\sqrt{x_1}\ne \sqrt{x_2}$ (Since square rooting a unique number results in a unique root.) So the function would not have the same $y$ value for two different $x$ values (one-to-one).