Answer
$f^{-1}(x)=\sqrt[3]{x+3}$
Work Step by Step
Step 1: Replace $f(x)$ with $y$.
$y=x^{3}-3$
Step 2: Interchange $x$ and $y$.
$x=y^{3}-3$
Step 3: Solve the equation for $y$.
$ x=y^{3}-3,\qquad$ ... add 3,
$ x+3=y^{3},\qquad$ ... take the third root,
$\sqrt[3]{x+3}=y$
Step 4: Replace y with the notation $f^{-1}(x)$.
$f^{-1}(x)=\sqrt[3]{x+3}$
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