Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.7 - Inverse Functions - 2.7 Exercises - Page 229: 70


$f^{-1} (x)= \dfrac{-5x-3}{(2x-5)}=\dfrac{-(5x+3)}{(2x-5)}$

Work Step by Step

When we apply the horizontal test, it has been noticed that the function is one-to-one and verifies the horizontal test. Therefore, the function has an inverse function. To compute the inverse, we will have to interchange $x$ and $y$. $x=\dfrac{5y-3}{2y+5} \implies 2xy-5y=-5x-3$ or, $y(2x-5)=-5x-3 \implies y= \dfrac{-5x-3}{(2x-5)}$ Replace $y$ with $f^{-1} (x)$. so, $f^{-1} (x)= \dfrac{-5x-3}{(2x-5)}=\dfrac{-(5x+3)}{(2x-5)}$
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