Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 258: 47

Answer

Step 1. $\sqrt {x+4}+\sqrt {x-1}$, $[1,\infty)$. Step 2. $\sqrt {x+4}-\sqrt {x-1}$, $[1,\infty)$. Step 3. $\sqrt {x^2+3x-4}$, $[1,\infty)$. Step 4. $\sqrt {\frac{x+4}{x-1}}$, $(1,\infty)$.

Work Step by Step

Step 1. Given $f(x)=\sqrt {x+4}$ with $x\geq-4$ and $g(x)=\sqrt {x-1}$ with $x\geq1$, we have $f+g=\sqrt {x+4}+\sqrt {x-1}$ with a domain of $x\geq1$ or $[1,\infty)$. Step 2. We have $f-g=\sqrt {x+4}-\sqrt {x-1}$ with a domain of $x\geq1$ or $[1,\infty)$. Step 3. We have $f\cdot g=\sqrt {x+4}\sqrt {x-1}=\sqrt {x^2+3x-4}$ with a domain of $x\geq1$ or $[1,\infty)$. Step 4. We have $\frac{f}{g}=\frac{\sqrt {x+4}}{\sqrt {x-1}}=\sqrt {\frac{x+4}{x-1}}$ with a domain of $x\gt1$ or $(1,\infty)$. (remove $x=1$ from above)
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