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 271: 70

Answer

If two functions are inverses of each other, then their product is the identity function.

Work Step by Step

If the domain of one function is the range of other function and vice versa, then they are inverse functions of each other. If $f\left( g\left( x \right) \right)=g\left( f\left( x \right) \right)=x$ is satisfied, f and g are inverse functions of each other. Suppose, ${{f}^{-1}}$ be an inverse function of f. Again let the function $y=f\left( x \right)$ Take the inverse on both sides, ${{f}^{-1}}\left( y \right)={{f}^{-1}}\left( f\left( x \right) \right)$ But ${{f}^{-1}}\left( f\left( x \right) \right)=x$ Thus, ${{f}^{-1}}\left( f\left( x \right) \right)=x={{f}^{-1}}\left( y \right)$ can be determined.
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