Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Practice Exercises - Page 37: 40

Answer

See graph and explanations.

Work Step by Step

Step 1. Graph the piece-wise function as shown in the first figure. Step 2. For $x\in[-2,-1]$, $f(x)\in[-1,0]$, thus $f(f(x))=(x+1)+1=x+2$ Step 3. For $x\in[-1,0)$, $f(x)\in[0,1)$, thus $f(f(x))=(x+1)-1=x$ Step 4. For $x\in[0,1]$, $f(x)\in[-1,0]$, thus $f(f(x))=(x-1)+1=x$ Step 5. For $x\in[1,2)$, $f(x)\in[0,1]$, thus $f(f(x))=(x-1)-1=x-2$ Step 6. Graph the composite $f(f(x))$ based on the above results as shown in the second figure.
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