Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 2 - Mid-Chapter Check Point - Page 135: 22

Answer

$(-\infty,-\frac{5}{2})\; or \;(-\frac{5}{2},\infty)$.

Work Step by Step

The given functions are $f(x)=x^2-3x+8$ and $g(x)=-2x-5$. $\Rightarrow \frac{f}{g}=\frac{f(x)}{g(x)}$ $\Rightarrow \frac{f}{g}=\frac{x^2-3x+8}{-2x-5}$ The value of the function $g(x)$ must not be equal to zero. Set the denominator equal to zero. $\Rightarrow -2x-5=0$ Add $5$ to both sides. $\Rightarrow -2x-5+5=0+5$ Simplify. $\Rightarrow -2x=5$ Divide both sides by $-2$. $\Rightarrow \frac{-2x}{-2}=\frac{5}{-2}$ Simplify. $\Rightarrow x=-\frac{5}{2}$ Exclude the above value. Hence, the domain of $\frac{f}{g}$ is $(-\infty,-\frac{5}{2})\; or \;(-\frac{5}{2},\infty)$.
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