Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 386: 5


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Work Step by Step

To find the inverse of $f(x)=\frac{x-2}{x-1}$, we have $$y=\frac{x-2}{x-1}\Longrightarrow yx-y=x-2\Longrightarrow x=\frac{y-2}{y-1}.$$ So the inverse function is given by $$f^{-1}(x)=\frac{x-2}{x-1}.$$ Its domian is $R-\{1\}$ and the range is also $R-\{1\}$.
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