Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Section 1.11 - Solving Equations and Inequalities Graphically - 1.11 Exercises - Page 122: 38

Answer

$$x ∈ (-\infty, -0.53] ∪ [0.53, +\infty)$$ Also see the image below.

Work Step by Step

$\sqrt{0.5x^2+1}\leq 2|x|$ $\sqrt{0.5x^2+1}$ is represented as the Blue graph on the image above. $2|x|$ is the Red graph on the image above. We need to find the region, where the Blue graph is below the Red graph. As we see from the image, these regions are: $(-\infty, -0.53] ∪ [0.53, +\infty)$
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