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: 73

Answer

$(-3, +\infty)$

Work Step by Step

RECALL: The logarithmic function $f(x) = \log_a{(x+h)}$ is defined only when $x+h$ is greater than $0$. This means that the given function is only defined when $x+3$ is greater zero. Thus, $x+3 \gt 0 \\x \gt 0-3 \\x \gt -3$ Therefore, the domain of the given function is $x \gt -3$ In interval notation, the domain is $(-3, +\infty)$.
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