Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.3 - Multiplying and Simplifying Radical Expressions - Exercise Set: 34

Answer

$f(x) = 9|x-2|$

Work Step by Step

Write 81 as $9^2$, and then simplify to obtain: $f(x)=\sqrt{9^2(x-2)^2} \\f(x)=9\sqrt{(x-2)^2}$ RECALL: (i) $\sqrt{a^2} = a$ when $a \ge 0$ (ii) $\sqrt{a^2} = |a|$ when $a \lt 0$ $x$ can be any real number. This means that when $x \lt 2$, the value of $x-2$ is negative. Thus, to simplify $f(x)=9\sqrt{(x-2)^2}$, rule (ii) above must be used. Therefore, $f(x) = 9|x-2|$
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