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 289: 74

Answer

$\color{blue}{\bf{(a) 24x+4; }}$$\color{blue}{\bf{ (-\infty,\infty) }}$ $\color{blue}{\bf{(b) 24x+35 ; }}$$\color{blue}{\bf{ (-\infty,\infty) }}$

Work Step by Step

We are given the two functions $\bf{f}$ and $\bf{g}$ $\bf{f(x) = 8x + 12 }$ and $\bf{g(x) = 3x - 1 }$ $\bf(a)$We are asked to find $\bf{ ( f \text{ }\omicron\text{ g} )( x ) }$ and its domain. ${ ( f \text{ }\omicron\text{ g} )( x ) }= 8( 3x - 1) + 12 $ $ 8( 3x - 1) + 12 $ $24x-8+12$ $\color{blue}{\bf{ 24x+4}}$ The domain is any real number or: $\color{blue}{\bf{ (-\infty,\infty) }}$ $\bf(b)$We are asked to find $\bf{ ( g \text{ }\omicron\text{ f} )( x ) }$ and its domain. ${ ( g \text{ }\omicron\text{ f} )( x ) }= 3(8x + 12 ) - 1 $ $ 3(8x + 12 ) - 1 $ $24x+36-1$ $\color{blue}{\bf{ 24x+35 }}$ The domain is any real number or: $\color{blue}{\bf{ (-\infty,\infty) }}$
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