# Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 228: 7

$f^{-1}[f (x)]=f[f^{-1} (x)]$, that is, the function is the inverse function.

#### Work Step by Step

We are given the function: $f(x)=6x \implies f^{-1} (x)=\dfrac{x}{6}$ Therefore, $f[f^{-1} (x)]=f[\dfrac{x}{6}]=6(x/6)=x$ and $f^{-1}[f (x)]=f^{-1}(6x)=6(x/6)=x$ Therefore, it has been verified that $f^{-1}[f (x)]=f[f^{-1} (x)]$, that is, the function is the inverse function.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.