Answer
$f^{-1}(x)=\sqrt[3]{x}-2$
Work Step by Step
The given function, $
f(x)=(x+2)^3
,$ is equivalent to
\begin{array}{l}\require{cancel}
y=(x+2)^3
\
.\end{array}
Interchanging the $x$ and $y$ variables, and then solving for $y$ result to
\begin{array}{l}\require{cancel}
x=(y+2)^3
\\\\
\sqrt[3]{x}=\sqrt[3]{(y+2)^3}
\\\\
\sqrt[3]{x}=y+2
\\\\
\sqrt[3]{x}-2=y
\\\\
y=\sqrt[3]{x}-2
.\end{array}
Hence, the inverse function is $
f^{-1}(x)=\sqrt[3]{x}-2
$.
