#### Answer

$f(x)$ has an inverse function.

#### Work Step by Step

We use the power rule to find the derivative of $f(x)$.
\[ f'(x) = 3x^2 - 12x+12 \]
We complete the square to get:
\[ f'(x) = 3(x-2)^2 \]
We see that $f'(x)$ is always nonzero because $(x-2)^2$ is always nonzero so $f(x)$ is strictly monotonic.