Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Review - Exercises - Page 232: 18

Answer

$(-1, +\infty)$

Work Step by Step

The given function is undefined when: (i) the denominator of $\dfrac{2}{\sqrt{x+1}}$ is equal to 0; and (ii) the radicand $x+1$ is negative. Note that: (1) The denominator $\sqrt{x+1}$ is equal to 0 when $x=-1$. (2) The radicand $x+1$ is negative when $x \lt -1$. Thus, the given function is defined when $x$ is greater than $-1$. Since $x$ cannot be less than or equal to $-1$, then the domain of the given function is the set of real numbers greater than $-1$. In interval notation, the domain is $(-1, +\infty)$.
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