Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.2 Domain and Range - 7.2 Exercise Set - Page 459: 42


Domain = $\mathbb{R}\backslash\{1\}$ or $\{x\in \mathbb{R}\ |\ x\neq 1\}$

Work Step by Step

The domain of a real function ( a function defined on real numbers) is the set of numbers for which f(x) is defined. $ f(x)=\displaystyle \frac{x}{x^{2}-2x+1}\quad$ can be calculated for any real number, except for those yielding a zero in the denominator. Here, $ x^{2}-2x+1=0\quad$ ... recognize a perfect square $(x-1)^{2}=0$ $x=1 \quad $must be excluded from the domain. Domain = $\mathbb{R}\backslash\{1\}$ or $\{x\in \mathbb{R}\ |\ x\neq 1\}$
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