Elementary Algebra

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

Chapter 11 - Additional Topics - Chapter 11 Review Problem Set: 77

Answer

The domain of this function is $\text{all real numbers where}\;x\ne-\frac{1}{3}$.

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 $\frac{3}{x}$, $x≠0$ 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 $\frac{2}{3x+1}$, we can't substitute $-\frac{1}{3}$ into the function as it would cause the denominator to be $3(-\frac{1}{3})+1=-1+1=0$, making the fraction undefined. Therefore, the domain of this function is $\text{all real numbers where}\;x\ne-\frac{1}{3}$.
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