College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 2 - Functions and Graphs - Exercise Set 2.6 - Page 298: 49

Answer

$f+g,f-g,fg$: for all Domain=$\{ x|x=2\}$. $\frac{f}{g}$: the domain is the empty set.

Work Step by Step

$f(x)=\sqrt {x-2}$ and $g(x)=\sqrt {2-x}$. $f(x)+g(x)=\sqrt {x-2} + \sqrt {2-x}$. To find the domain of the sum function, $x-2\geq0$, $x\geq2$ and $2-x\geq0$, $x\leq2$. Therefore, Domain=$\{ x:x=2\}$. $f(x)-g(x)=\sqrt {x-2} - \sqrt {2-x}$. To find the domain of the difference function, $x-2\geq0$, $x\geq2$ and $2-x\geq0$, $x\leq2$. Therefore, Domain=$\{ x:x=2\}$. $f(x) \times g(x)=\sqrt {x-2} \times \sqrt {2-x}=\sqrt {(x-2)(2-x)}$. To find the domain of the product function, $x-2\geq0$, $x\geq2$ and $2-x\geq0$, $x\leq2$. Therefore, Domain=$\{ x:x=2\}$. $\frac{f(x)}{g(x)}=\frac{\sqrt {x-2}}{\sqrt {2-x}}=\sqrt {\frac{x-2}{2-x}}$.To find the domain of the quotient function, $x-2\geq0$, $x\geq2$ and $2-x\gt0$, $x\lt2$ .Therefore, Domain=$\{ x:x=\{\}\}$. The domain is the empty set.
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