Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 260: 109

Answer

See graph and explanations.

Work Step by Step

Step 1. Graph the function $y_1=\sqrt {2-x}$ as the blue curve in the figure. Step 2. Graph the function $y_2=\sqrt x$ as the green curve in the figure. Step 3. Graph the composite function $y_3=\sqrt {2-y_2}$ as the red curve in the figure. Step 4. We can identify the domain of $f\circ g$ as $[0,4]$ Step 5. Algebraically, we have $f\circ g=\sqrt {2-\sqrt x}$ and the domain requirement is that $2-\sqrt x\geq0$ which requires $0\leq x\leq 4$ or $[0,4]$
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