Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.7 - Relations and Functions - Problem Set 11.7 - Page 508: 28


The domain of this function is $\text{All real numbers where}\;x\ne0$.

Work Step by Step

When this question asks for the domain of the function, it is asking for the values of $x$ that can be legally substituted into the function. (For instance, in the function $\frac{1}{x}$, $x\ne0$ because this would make the denominator of the fraction equal to 0, making the function at that value be undefined.) In the case of the function $y=\frac{x-4}{2x}$, we can't substitute $0$ into the function as it would cause the denominator to be $2\times0=0$, making the fraction undefined. Therefore, the domain of this function is $\text{All real numbers where}\;x\ne0$.
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