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: 102


a. see explanations. b. $0.6x-5$, see explanations. c. $0.6(x-5)$, see explanations. d. $(f\circ g)(x)$, see explanations.

Work Step by Step

a. Given $x$ as the price of a pair of jeans, we can describe $f(x)=x-5$ as: the price of a pair of jeans after a $5$ dollar discount. Similarly, we can describe $g(x)=0.6x$ as the price of a pair of jeans after a $40\%$ discount. b. We can find $(f\circ g)(x)=0.6x-5$, which means a $40\%$ discount followed by a $5$ dollar discount. c. We can find $(g\circ f)(x)=0.6(x-5)$, which means a $5$ dollar discount followed by a $40\%$ discount. d. As $(f\circ g)(x)-(g\circ f)(x)=-5+3=-2$, the composite $(f\circ g)(x)$ has a bigger discount (lower price).
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