College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 2 - Summary, Review, and Test - Review Exercises - Page 326: 86

Answer

$g$ and $f$ are inverses of each other

Work Step by Step

$f(x)=2-5x$ and $g(x)=\frac{2-x}{5}$ $f(g(x))=2-5(\frac{2-x}{5})=2-2+x=x$ $g(f(x))=\frac{2-(2-5x)}{5}=\frac{2-2+5x}{5}=x$ As $$f(g(x))=g(f(x))\not=x$$ it follows that $g$ and $f$ are inverses of each other.
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