## Algebra and Trigonometry 10th Edition

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