College Algebra (10th Edition)

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

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding - Page 449: 45

Answer

$(-1, +\infty)$

Work Step by Step

Recall: The function $y=\ln{x}$ is defined only when $x\gt0$. Thus, the function $f(x)=\ln{\frac{1}{x+1}}$ is defined only when $\dfrac{1}{x+1}\gt0$. Note that $\dfrac{1}{x+1}$ is greater than zero then $x+1\gt0$. Hence, the given function is defined only when: \begin{align*} x+1&\gt0\\ x&\gt -1 \end{align*} Therefore, the domain of the given function is $(-1, +\infty)$.
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