To do this, we switch the roles of $x$ and $y$ in the equation $f(x) = x^3 - 3x^2 - 1$ and solve for $x$:
$$x = y^3 - 3y^2 - 1$$
Now, we solve this equation for $y$ to find $f^{-1}(x)$:
$$y^3 - 3y^2 - 1 - x = 0$$
This is a cubic equation in $y$, which can be
Show more…