Answer
$$f^{-1}(x)=\sqrt[3]{x+1}$$
Work Step by Step
$$y=f(x)=x^3-1$$
To find its inverse:
1) Solve for $x$ in terms of $y$:
$$y = x^3-1$$ $$x^3=y+1$$ $$x=\sqrt[3]{y+1}$$
2) Interchange $x$ and $y$:
$$y=\sqrt[3]{x+1}$$
Therefore, the inverse of function $y=f(x)=x^3-1$ is the function $y=\sqrt[3]{x+1}$. In other words, $$f^{-1}(x)=\sqrt[3]{x+1}$$
