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: 39

Answer

$(-1/2, 0) U (1/2, ∞)$

Work Step by Step

Values of x in which $f(x) > g(x)$ Given $f(x) = 4x$ and $g(x) = \frac {1}{x}$ $4x > \frac{1}{x-1}$ $4x - \frac {1}{x} > 0 $ $\frac {4x^2 - 1}{(x)} > 0$ $\frac {(2x-1)(2x+1)}{x} > 0$ Find the zeros of the expressions in the numerator AND the denominator $x = -1/2, 1/2, 0$ Test numbers in between those zero values to determine if the function is negative or positive (-∞, -1/2) $\frac {(-)(-)}{(-)} = (-)$ (-1/2, 0) $\frac {(-)(+)}{(-)} = (+)$ (0, 1/2) $\frac {(-)(+)}{(+)} = (-)$ (1/2, ∞) $\frac {(+)(+)}{(+)} = (+)$ Thus the solution is $(-1/2, 0) U (1/2, ∞)$
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