#### Answer

$f(x)$ has an inverse function on the given interval.

#### Work Step by Step

We find the derivative of $f(x)$:
\[ f'(x) = \sec(x)\tan(x) \]
On the domain $[0, \frac{\pi}{2})$, both $\sec(x)$ and $\tan(x)$ are nonnegative so $f'(x)$ is nonnegative. Therefore $f(x)$ is strictly monotonic.