Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.1 - Radical Expressions and Functions - Exercise Set - Page 513: 97



Work Step by Step

Let $f(x)=\sqrt {x-1}$ and $g(x)=\dfrac{1}{\sqrt{3-x}}$ In order to find the domain we will have to set the equation inside the square root greater than and equal to zero. we have, $\sqrt {x-1} \geq 0$ and $\sqrt{3-x} \geq 0$ or, $x-1 \geq 0$ and $(\sqrt{3-x})^2 \geq (0)^2$ or, $x \geq 1$ and $3-x \geq 0$ or, $x \geq 1$ and $x \lt 3$ Thus, Domain for $\dfrac{f(x)}{g(x)}$ will be a set of interval to both domains, that is, $[1,3)$
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