Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 352: 74


$(-\infty, 4)$

Work Step by Step

RECALL: The logarithmic function $f(x) = \log_a{x}$ is defined only when $x$ is greater than $0$. This means that the given function is only defined when $8 - 2x$ is greater than zero. Thus, $8-2x \gt 0 \\-2x \gt 0-8 \\-2x \gt -8$ Divide $-2$ to both sides of the inequality. Note that the inequality symbol will flip too the opposite direction since a negative number was divided to each side. $x \lt \frac{-8}{-2} \\x \lt 4$ Therefore, the domain of the given function is $x \lt 4$ In interval notation, the domain is $(-\infty, 4)$.
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