Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.3 - Radicals and Rational Exponents - Exercise Set - Page 47: 127

Answer

See explanations.

Work Step by Step

Step 1. The domain requirement for a square root function $f(x)=\sqrt x$ is that $x\geq0$ or $x$ be nonnegative. Step 2. For $\sqrt a\sqrt b=\sqrt {ab}$ to be valid, each term needs to be defined, which requires values $a$ and $b$ to be nonnegative. Step 3. In the case of $g(x)=\sqrt[3] x$, the domain contains all the real numbers, including negative numbers; thus the formula $\sqrt[3] a\sqrt[3] b=\sqrt[3] {ab}$ does not require nonnegative values of $a$ and $b$.
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