Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.8 Function Operations and Composition - 2.8 Exercises - Page 290: 99

Answer

$\color{blue}{\bf{ f(x)= \sqrt{x} \text{ ; } g(x)= x^2-1 }}$ $\color{blue}{\bf{\text{or other equivalent functions}}}$

Work Step by Step

We are given the function $\bf{h(x)= \sqrt{x^2-1} }$ and are asked to find two functions ${f(x)}$ and ${g(x)}$ such that $( f \text{ }\omicron\text{ g} )(x) =h(x)$ There are many ways to do this, for example: $\color{magenta}{f(x)= \sqrt{x} }$ and $\color{lime}{g(x)= x^2-1 }$ $\color{magenta}{ \sqrt{ \color{lime}{ x^2-1 } } }$ $\color{blue}{\bf{ f(x)= \sqrt{x} \text{ ; } g(x)= x^2-1 }}$ $\color{blue}{\bf{\text{or other equivalent functions}}}$
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