College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.7 - Combining Functions - 2.7 Exercises - Page 252: 18


$[-4,\ 0) \cup (0, 1]$

Work Step by Step

We are given: $f(x)=\displaystyle \sqrt{x+4}-\frac{\sqrt{1-x}}{x}$ The domain of $\sqrt{x+4}$ is: $[-4,\ \infty$) (since $x$ must be greater or equal to -4 to avoid a negative root). The domain of $\displaystyle \frac{\sqrt{1-x}}{x}$ is: $(-\infty,\ 0)\cup (0, 1]$ (since $x$ must be less than or equal to 1 to avoid a negative root and not 0). Therefore, the domain of $f(x)$ is the intersection of the two domains above: $[-4,\ 0) \cup (0, 1]$.
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