Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Review Exercises - Page 303: 92


The domain of the function $g\left( x \right)=\frac{4}{x-7}$ is $\left( -\infty,7 \right)\cup \left( 7,\infty \right)$.

Work Step by Step

Consider the given function $g\left( x \right)=\frac{4}{x-7}$. We can see that this function contains division and division by 0 is not defined, excluding those values of $x$ from the domain that cause the denominator to be zero. Thus, set the denominator equal to 0, that is, $x-7=0$. This means that $x=7$. Therefore, the domain of the given function is the set of all real numbers excluding the number 7. Thus, the domain of the function $g\left( x \right)=\frac{4}{x-7}$ is $\left( -\infty,7 \right)\cup \left( 7,\infty \right)$.
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