Answer
$f(g(x))=x$ and $g(f(x))=x$.
Work Step by Step
$f(x)=4x+9, g(x)=\frac{x-9}{4}$
$f(g(x))=4\left(\frac{x-9}{4}\right)+9=x$
and
$g(f(x))=\frac{4x+9-9}{4}=x$.
$f(g(x))=g(f(x))=x.$
Thus, $f(x)$ and $g(x)$ are Inverse of each other.
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13417-894-7
ISBN 13:
978-0-13417-894-3
Chapter 9 - Section 9.2 - Composite and Inverse Functions - Exercise Set - Page 686: 18
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