## Calculus 10th Edition

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