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: 101


a. See explanations. b. $0.75x-400$. See explanations. c. $0.75(x-400)$. See explanations. d. $(f\circ g)(x)$. See explanations.

Work Step by Step

a. Given $x$ as the price of a computer, we can describe $f(x)=x-400$ as the situation: there is a $400$ dollar discount for the computer. And for $g(x)=0.75x$, we can describe the situation as: there is a $25\%$ discount in the computer price. b. We can find $(f\circ g)(x)=(0.75x)-400=0.75x-400$, which can be described as: the computer price has a $25\%$ discount and then another $400$ dollar discount. c. We can find $(g\circ f)(x)=0.75(x-400)$, which can be described as: the computer price has a $400$ dollar discount and then another $25\%$ discount. d. Evaluate $(f\circ g)(x)-(g\circ f)(x)=-400+0.75(400)=-100$, which means that $(f\circ g)(x)$ has a bigger discount (lower price).
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