Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Review - Test - Page 138: 15

Answer

For $x$ in the interval $[0,6]$

Work Step by Step

Complex (unreal) numbers are used when we cannot define a specific number; when it has no real definition. For example, even root of a negative number. $\sqrt{6x-x^2}$ The expression above is defined as a real number when the expression inside square root is non-negative number, that is: $6x-x^2\geq 0$ $x(6-x)\geq 0$ We can solve the inequality using intervals method. We have two critical points (Those are the points where the expression is equal to $0$) and three intervals: $x_1=0$ $x_2=6$ $(-\infty, 0]$ - Negative $[0, 6]$ - Positive $[6, +\infty)$ - Negative Our solution is in the interval: $[0,6]$
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