Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 8 - Radical Functions - Chapter Review Exercises - Page 669: 12

Answer

Domain: $x\geq 0$ Range: $y\leq 0$

Work Step by Step

Given \begin{equation} M(p)=-2.3 \sqrt[6]{p}. \end{equation} The radicand of an even radical function must be positive. This means that we must have $x\geq 0$. Also, we see that the function's value $y=M(p)$ must satisfy $y\leq 0$ because $$\sqrt[6]{p}\geq 0\implies 2.3\sqrt[6]{p}\geq 0\implies -2.3\sqrt[6]{p}\leq 0.$$ We got: \begin{equation} \begin{aligned} \textbf{Domain :}\quad & p\geq 0\\ \textbf{Range :}\quad & y\leq 0\\\\ \end{aligned} \end{equation}
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