Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Review: 28

Answer

$ r^{-1}(x)=\frac{2x+5}{13}$

Work Step by Step

We are given the function, $r(x)=\frac{13x-5}{2}$. First, we must replace $r(x)$ with y. $y=\frac{13x-5}{2}$ Next, interchange x and y. $x=\frac{13y-5}{2}$ Next, multiply both sides by 2. $2x=13y-5$ Add 5 to both sides. $13y=2x+5$ Divide both sides by 13. $y=\frac{2x+5}{13}$ Finally, replace y with $r^{-1}(x)$. $ r^{-1}(x)=\frac{2x+5}{13}$
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