Precalculus (6th Edition) Blitzer

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

Chapter 1 - Review Exercises - Page 303: 96


The domain of the function $f\left( x \right)=\sqrt{x-1}\text{ +}\sqrt{x+5}$ is $\left[ 1,\infty \right)$.

Work Step by Step

Consider the function, $f\left( x \right)=\sqrt{x-1}\text{ +}\sqrt{x+5}$ Since, this function involves the square root and the square root of a negative real number is not defined, the expression written inside the square root sign must be non-negative, that is, $x-1\ge 0$ or $x\ge 1$. Also, $x+5\ge 0$ or $x\ge -5$. Therefore, the domain of the function $f\left( x \right)=\sqrt{x-1}\text{ +}\sqrt{x+5}$ is $\left[ 1,\infty \right)$.
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