College Algebra 7th Edition

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

Chapter 2, Functions - Section 2.1 - Functions - 2.1 Exercises - Page 193: 65


$[-2, 3) \cup (3,\ \infty)$

Work Step by Step

We are given: $g(x)= \frac{\sqrt{2+x}}{3-x}$ The domain of a function consists of all values that $x$ is allowed to have. In this case, we can not take the square root of a negative number, so: $2+x\geq 0$ $ x\geq-2$ We also can not have division by $0$: $3-x\neq 0$ $ x\neq 3$ Therefore, the domain is: $[-2, 3) \cup (3,\ \infty)$
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