Answer
$f^{-1}(x)=\sqrt[3]{x+1}$
The graph of both functions is shown below:
Work Step by Step
$f(x)=x^{3}-1$
Substitute $f(x)$ by $y$:
$y=x^{3}-1$
Solve for $x$. Begin by taking $-1$ to the left side:
$y+1=x^{3}$
$x^{3}=y+1$
Take the cubic root of both sides:
$\sqrt[3]{x^{3}}=\sqrt[3]{y+1}$
$x=\sqrt[3]{y+1}$
Interchange $x$ and $y$:
$y=\sqrt[3]{x+1}$
Substitute $y$ by $f^{-1}(x)$:
$f^{-1}(x)=\sqrt[3]{x+1}$
