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: 42

Answer

$[-5, 5) $

Work Step by Step

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