## Calculus 10th Edition

$f(x)$ has an inverse function.
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.