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: 69

Answer

The functions f and g are inverse functions of each other.

Work Step by Step

Suppose the available expression is: $f\left( x \right)=\frac{9}{5}x+32$ and $g\left( x \right)=\frac{5}{9}(x-32)$ Now solve for$f\left( g\left( x \right) \right)$ $f\left( g\left( x \right) \right)=$$\frac{9}{5}\left( \frac{5}{9}\left( x-32 \right) \right)+32$ $f\left( g\left( x \right) \right)=x$ …. (1) Again solve for $g\left( f\left( x \right) \right)$ $g\left( f\left( x \right) \right)=\frac{5}{9}\left( \left( \frac{9}{5}x+32 \right)-32 \right)$ $g\left( f\left( x \right) \right)=x$ …. (2) But, from (1) and (2) $g\left( f\left( x \right) \right)=f\left( g\left( x \right) \right)=x$ So, f and g are inverse functions to each other. Thus, the functions f and g are inverse functions of each other.
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