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: 24

Answer

The domain of the given function is the set of all real numbers except $\frac{-3}{7}$.

Work Step by Step

When the question asks for the domain of the function, it is asking for what values of x can be legally substituted into the function. (For instance, in the function $\frac{2}{x}$, x $\ne$ 0, for this would make the denominator of the fraction equal to 0.) Look for the number that makes the denominator zero by equating the denominator to 0: $7x+3=0 \\7x = 0-3 \\7x=-3 \\x = \frac{-3}{7}$ Thus, when $x=\frac{-3}{7}$, the denominator is equal to zero. Therefore, the domain of the given function is the set of all real numbers except $\frac{-3}{7}$.
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