Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.6 - Combinations of Functions: Composite Functions - 2.6 Exercises - Page 219: 9


a) $x^2+6+\sqrt{1-x}$ b) $x^2+6-\sqrt{1-x}$ c) $(x^2+6)\sqrt{1-x}$ d) $\dfrac{x^2+6}{\sqrt{1-x}}$ Domain: $\left(-\infty,1\right)$

Work Step by Step

We are given the functions: $f(x)=x^2+6$ $g(x)=\sqrt{1-x}$ a) Determine $(f+g)(x)$: $(f+g)(x)=f(x)+g)(x)=x^2+6+\sqrt{1-x}$ b) Determine $(f-g)(x)$: $(f-g)(x)=f(x)-g)(x)=x^2+6-\sqrt{1-x}$ c) Determine $(fg)(x)$: $(fg)(x)=f(x)g)(x)=(x^2+6)\sqrt{1-x}$ d) Determine $\left(\dfrac{f}{g}\right)(x)$: $\left(\dfrac{f}{g}\right)(x)=\dfrac{x^2+6}{\sqrt{1-x}}$ The domain of $\dfrac{f}{g}$ is the set of all real numbers except the zeros of $g$ and the values of $x$ for which the radical is undefined: $1-x\gt 0\Rightarrow x\lt 1$ The domain is: $\left(-\infty,1\right)$
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