Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set: 49

Answer

$(-\infty, 2)$

Work Step by Step

RECALL: The domain of the logarithmic function $f(x) = \log_a{x}$ is $x \gt 0$. Thus, the domain of the given function is the set of all real numbers such that: $2-x \gt 0$. Solve the inequality to obtain: $2-x \gt 0 \\-x \gt 0-2 \\-x \gt -2 \\(-1)(-x) \lt -2(-1) \\x \lt 2$ (Note that the inequality sign flips when we multiply by a negative number on both sides of the inequality.) Therefore, the domain of the given function is $(-\infty, 2)$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.