Answer
It has been verified that $f^{-1}[f (x)]=f[f^{-1} (x)]$, that is, the function is the inverse function.
So, the inverse function is: $3x$
Work Step by Step
We have the inverse function: $f^{-1} (x)=3x$
Therefore, $f[f^{-1} (x)]=f(3x)=\dfrac{3x}{3}=x$
and $f^{-1}[f (x)]=f^{-1}(\dfrac{x}{3})=3(\dfrac{x}{3})=x$
Therefore, it has been verified that $f^{-1}[f (x)]=f[f^{-1} (x)]$, that is, the function is the inverse function.
So, the inverse function is: $3x$
