Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises: 82

Answer

$-\sqrt{2} < x < \sqrt{2}$

Work Step by Step

Factor out $e^{x}:$ $e^{x}(x^{2}-2) < 0$ The function $f(x)=e^{x}$ is always positive, never zero, so LHS $ < 0$ only if $x^{2}-2 < 0$ $x^{2}<2$ This is valid only if $|x| < 2$, that is, if $-\sqrt{2} < x < \sqrt {2}$
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