Answer
$f(x)$ has an inverse function on the given interval.
Work Step by Step
There is a cusp at $x = -2$ so we'll differentiate $f(x)$ from $(-\infty, -2]$.
\[ f'(x) = -1 \]
$f'(x)$ is always negative from $(-\infty, -2]$ so $f(x)$ is strictly monotonic.
