#### Answer

$f(x)$ does not have an inverse function.

#### Work Step by Step

We use the power rule to find the derivative of $f(x)$.
\[ f'(x) = x^3 - 4x = x(x^2-4) = x(x+2)(x-2) \]
$f'(x)$ can be both positive and negative so $f(x)$ is not strictly monotonic on its entire domain.