# Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 228: 8

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: $3x$

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