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 219: 60

Answer

$[-1,0] \cup [1,\infty)$

Work Step by Step

$x^3-x\geq0\\x(x-1)(x+1)\geq0$ The zeros from $x(x-1)(x+1)=0$: $x=0$ or $x-1=0\\x=1\\$ or $x+1=0\\x=-1$. I use the real zeros and the values for which the function is undefined to separate the real number line into different intervals: $(-\infty,-1)$,$(-1,0)$, $(0,1)$, $(1,\infty)$. I now select a test number in each interval found in the step above and evaluate the function on the left side of the inequality at each number to determine if the function is positive or negative. Refer to the table for this. According to the table the solution set: $[-1,0] \cup [1,\infty)$ because the function is non-negative in this interval.
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