Answer
Yes, g(x) is one-to-one
Work Step by Step
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).
