Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.4 Polynomial and Rational Inequalities - 4.4 Assess Your Understanding - Page 220: 70

Answer

$(-\infty,-4)U[1,\infty)$

Work Step by Step

Step 1. The domain requirements for this function is $\frac{x-1}{x+4}\ge0$ Step 2. The boundary points are $x=-4,1$ dividing the x-axis into $(-\infty,-4),(-4,1],[1,\infty)$ Step 3. Use test values $x=-5,0,2$ to test the inequality and we can get the result as $True,\ False,\ True$ Step 4. Thus the domain is $(-\infty,-4)U[1,\infty)$
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