Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.7 - Polynomial and Rational Inequalities - 3.7 Exercises - Page 316: 43

Answer

$(-∞, -1] U [1, ∞) $

Work Step by Step

Given $f(x) = \sqrt[4] {x^4 - 1}$ In a even root function, the domain is defined such that the function is always at (if defined) or above 0, so $f(x) \geq 0$ $\sqrt[4] {x^4 -1} \geq 0$ $x^4 - 1 \geq 0$ $(x^2 - 1) (x^2 + 1) \geq 0$ $(x-1)(x+1)(x^2 + 1) \geq 0$ Find the zeros of the expression. $x = 1, -1$ Test numbers in between those zero values to determine if the function is negative or positive (-∞, -1] $(-)(-)(+) = (+)$ [-1, 1] $(-)(+)(+) = (-)$ [1, ∞) $(+)(+)(+) = (+)$ Thus the solution is $(-∞, -1] U [1, ∞) $
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