#### Answer

$f(x)$ has an inverse function.

#### Work Step by Step

We use the power rule to find:
\[ f'(x) = -3x^2 -1 \]
$x^2$ is always positive so $-3x^2$ is always positive. Therefore, $f'(x)$ is always negative, and $f(x)$ is strictly monotonic (it is always decreasing).