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