Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Section 2.7 - Combining Functions - 2.7 Exercises - Page 216: 20

Answer

$[-3,1)\cup(1+\infty)$

Work Step by Step

Interpret $f(x) $ as $\displaystyle \frac{u(x)}{v(x)}.$ The domain of f is the intersection of domains of u and v, with $v(x)\neq 0.$ Domain of $u(x)=\sqrt{x+3}$ is $x+3\geq 0$, or, the interval $[-3,+\infty)$ The domain of $v(x)$ is all reals, from which we exclude $x=1$, as it yields zero in the denominator. The domain of f is then, the interval $[-3,+\infty)$ excluding $x=1,$ that is, $[-3,1)\cup(1+\infty)$
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