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: 23

Answer

The domain of the given function is the set of all real numbers except $\frac{8}{5}$.

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.) Thus, we look for the number that makes the denominator zero by equating the denominator to 0: $5x-8=0 \\5x = 0+8 \\5x=8 \\x = \frac{8}{5}$ Thus, when $x=\frac{8}{5}$. the denominator is equal to zero. Therefore, the domain of the given function is the set of all real numbers except $\frac{8}{5}$.
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