Answer
Yes, $f(g(x)) = g(f(x))$ for some functions.
Work Step by Step
If we let $g(x)=x-1$ and $f(x)=x+1$, then
$g(f(x))=g(x+1)=(x+1)-1 = x+1-1= x$
$f(g(x)) = f(x-1) = (x-1)+1 = x-1+1 = x$
In this case, $f(g(x)) = g(f(x))$.
Intermediate Algebra (6th Edition)
by Martin-Gay, Elayn
Published by
Pearson
ISBN 10:
0321785045
ISBN 13:
978-0-32178-504-6
Chapter 9 - Section 9.1 - The Algebra of Functions; Composite Functions - Vocabulary, Readiness & Video Check - Page 540: 8
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