College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Review Exercises: 7

Answer

Domain: $\color{blue}{(-\infty, 2]}$

Work Step by Step

To find the domain of the given function, exclude the values of $x$ that will make the function undefined. Note that the function is undefined when the radicand (expression inside the radical sign) is negative. This is because the square root of a negative number is an imaginary number. This means that the value of $x$ can be any real number that will make the radicand greater than or equal to zero. Thus, $2-x \ge 0 \\-x \ge 0-2 \\-x \ge -2$ Multiply by $-1$ on both sides of the inequality. Note that this will flip the inequality symbol to the opposite direction. $x \le -2(-1) \\x \le 2$ Thus, the value of $x$ can be any real number less than or equal to $2$ . In interval notation, Domain: $\color{blue}{(-\infty, 2]}$
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