College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 14

Answer

$\left\{x|x\ge0\right\}$

Work Step by Step

The denominator of a rational expression cannot be zero so $x$ should not be equal to $-1$. The square root is only defined when the radicand (number or expression inside a radical sign) is non-negative. Thus, to find the numbers for which $\sqrt{2x}$ is defined, solve the inequality $2x \ge 0$ to obtain: $2x \ge 0 \\\frac{2x}{2} \ge \frac{0}{2} \\x \ge 0$ Having $x\ne -1$ and $x \ge 0$ mean that the domain of the give expression is any real number greater than or equal to 0.
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