Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.8 - Inverse Functions - Exercise Set - Page 272: 87



Work Step by Step

The above statement can be verified by applying the identity \[\underbrace{{{f}^{-1}}\left( f\left( x \right) \right)}_{\text{LHS}}=\underbrace{x}_{\text{RHS}}\] By solving the left hand side: ${f}^{-1}(f(x))=$ \[\begin{align} & \left( \frac{f\left( x \right)+4}{5} \right) \\ & \left( \frac{5x-4+4}{5} \right) \\ & \left( \frac{5x}{5} \right) \\ \end{align}\] $= (x)$ Thus, the left-hand side of the expression is equal to the right hand side of the expression $=x$
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