College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Test: 14

Answer

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

Work Step by Step

We are given: $f(x)=\displaystyle \frac{x-3}{2x+5}$ To find the inverse of $f$, we switch $x$ and $y$ and solve for $y$: $y= \frac{x-3}{2x+5}$ $x= \frac{y-3}{2y+5}$ $x(2y+5)=y-3$ $2xy+5x=y-3$ $5x+3=y-2xy$ $5x+3=y(1-2x)$ $y=\frac{5x+3}{1-2x}$ Therefore, the inverse is: $f^{-1}(x)=\frac{5x+3}{1-2x}$
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