Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 6 - Section 6.1 - Rational Expressions and Functions; Multiplying and Dividing - 6.1 Exercises: 6

Answer

a. {$x$|$x$ is a real number, $x\ne-\frac{7}{2}$} b. $(-∞,-\frac{7}{2})U(-\frac{7}{2},∞)$

Work Step by Step

We are given the function $f(x)=\frac{8x-3}{2x+7}$. The domain of the function will be all values of $x$ such that the denominator does not equal 0. Therefore, we can set the denominator equal to 0. We will exclude from the domain all values of $x$ that make the denominator equal 0. $2x+7=0$ Subtract 7 from both sides. $2x=-7$ Divide both sides by 2. $x=-\frac{7}{2}$ Therefore, the domain is {$x$|$x$ is a real number, $x\ne-\frac{7}{2}$} in set-builder notation and $(-∞,-\frac{7}{2})U(-\frac{7}{2},∞)$ in interval notation.
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