College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.4 - Average Rate of Change of a Function - 2.4 Exercises - Page 224: 21


(a) $\frac{1-a}{a}$ (b) $-\frac{1}{a}$

Work Step by Step

We are given: $g(x)=\frac{1}{x}$; $x=1$, $x=a$ (a) We calculate the net change: $g(a)-g(1)=\displaystyle \frac{1}{a}-\frac{1}{1}=\frac{1}{a}-\frac{a}{a}=\frac{1-a}{a}$ (b) We calculate the average rate of change: $\displaystyle \frac{g(a)-g(1)}{a-1}=\frac{\frac{1-a}{a}}{a-1}=\frac{1-a}{a(a-1)}=-\frac{a-1}{a(a-1)}=-\frac{1}{a}$
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