#### Answer

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

#### Work Step by Step

We find the derivative of $f(x)$:
\[ f'(x) = -\sin(x) \]
On the domain $[0 , \pi]$, $\sin(x)$ is always nonnegative so $f'(x)$ is always nonpositive on the same domain, and $f(x)$ is strictly monotonic.