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: 26

Answer

On $[0,2]$: $g(x)$ On $(6,\infty)$: $f(x)$

Work Step by Step

We are given the functions: $f(x)=\dfrac{x}{2}$ $g(x)=\sqrt x$ Determine the function $f+g$: $(f+g)(x)=f(x)+g(x)=\dfrac{x}{2}+\sqrt x$ Graph the functions $f$, $g$, and $f+g$: On the interval $[0,2]$, $g(x)$ contributes to the majority of the magnitude of $(f+g)(x)$. On the interval $(6,\infty)$, $f(x)$ contributes to the majority of the magnitude of $(f+g)(x)$.
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