College Algebra 7th Edition

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

Chapter 2, Functions - Section 2.1 - Functions - 2.1 Exercises - Page 193: 47

Answer

$f(a)=\frac{a}{a+1}$ $f(a+h)=\frac{a+h}{a+h+1}$ $\frac{f(a+h)-f(a)}{h}=\frac{1}{(a+h+1)(a+1)}$

Work Step by Step

We are given $f(x)=\frac{x}{x+1}$ We evaluate: $f(a)=\frac{a}{a+1}$ $f(a+h)=\frac{a+h}{a+h+1}$ $\frac{f(a+h)-f(a)}{h}=\frac{\frac{a+h}{a+h+1}-\frac{a}{a+1}}{h}=\frac{(a+h)(a+1)-a(a+h+1)}{(a+h+1)(a+1)h}=\frac{a^{2}+a+ah+h-a^{2}-ah-a}{(a+h+1)(a+1)h}=\frac{h}{(a+h+1)(a+1)h}=\frac{1}{(a+h+1)(a+1)}$
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