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: 44

Answer

$(-∞, -2) U (-1, 1) U (2, ∞) $

Work Step by Step

Given $f(x) =\frac {1}{ \sqrt {x^4 - 5x^2 + 4}}$ In a even root function, the domain is defined such that the function is always at (if defined) or above 0, so $f(x) \geq 0$ $\frac {1}{ \sqrt {x^4 - 5x^2 + 4}} \geq 0$ $\frac {1}{x^4 - 5x^2 + 4} \geq 0$ $\frac {1}{(x^2 - 4)(x^2 - 1)} \geq 0$ $\frac {1}{(x+2)(x+1)(x-1)(x-2)}) \geq 0$ Find the zeros of the expression. $x = -2, -1, 1, 2$ Test numbers in between those zero values to determine if the function is negative or positive (-∞, -2) $\frac{(+)}{(-)(-)(-)(-)} = (+)$ (-2, -1) $\frac{(+)}{(+)(-)(-)(-)} = (-)$ (-1, 1) $\frac{(+)}{(+)(+)(-)(-)} = (+)$ (1, 2) $\frac{(+)}{(+)(+)(+)(-)} = (-)$ (2, ∞) $\frac{(+)}{(+)(+)(+)(+)} = (+)$ Thus the solution is $(-∞, -2) U (-1, 1) U (2, ∞) $
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