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: 36


Domain = $\displaystyle \mathbb{R}\backslash\{-\frac{3}{4}\}$ or $\displaystyle \{x\in \mathbb{R}\ |\ x\neq-\frac{3}{4}\}$

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. $f(x)=\displaystyle \frac{2x}{4x+3}$ can be calculated for any real number, except for those yielding a zero in the denominator. Here, $4x+3=0$ $4x=-3$ $x=-\displaystyle \frac{3}{4} \quad $must be excluded from the domain. Domain = $\displaystyle \mathbb{R}\backslash\{-\frac{3}{4}\}$ or $\displaystyle \{x\in \mathbb{R}\ |\ x\neq-\frac{3}{4}\}$
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