Answer
$f^{-1}(x)=\sqrt[3]{x}+5$
Work Step by Step
The given function, $
f(x)=(x-5)^3
,$ is equivalent to
\begin{array}{l}\require{cancel}
y=(x-5)^3
\
.\end{array}
Interchanging the $x$ and $y$ variables, and then solving for $y$ result to
\begin{array}{l}\require{cancel}
x=(y-5)^3
\\\\
\sqrt[3]{x}=\sqrt[3]{(y-5)^3}
\\\\
\sqrt[3]{x}=y-5
\\\\
\sqrt[3]{x}+5=y
\\\\
y=\sqrt[3]{x}+5
.\end{array}
Hence, the inverse function is $
f^{-1}(x)=\sqrt[3]{x}+5
$.
