College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Review - Exercises - Page 270: 85

Answer

$(f\circ g)(x)=6x-3x^{2}-1$ $(g\circ f)(x)=-x^{2}+6x-2$ $(f\circ f)(x)=9x-4$ $(g\circ g)(x)=x^{4}+4x^{3}-6x^{2}+4x$ The domain of $(f\circ g)(x)$, $(g\circ f)(x)$, $(f\circ f)(x)$ and $(g\circ g)(x)$ are $ R $

Work Step by Step

We are given $f(x)=3x-1$ and $g(x)=2x-x^{2}$ Thus we have $(f\circ g)(x)=f(2x-x^{2})=3(2x-x^{2})-1=6x-3x^{2}-1$ $(g\circ f)(x)=g(3x-1)=2(3x-1)-x^{2}=-x^{2}+6x-2$ $(f\circ f)(x)=f(3x-1)=3(3x-1)-1=9x-4$ $(g\circ g)(x)=g(2x-x^{2})=2(2x-x^{2})-(2x-x^{2})^{2}=4x-2x^{2}-4x^{2}+4x^{3}-x^{4}=x^{4}+4x^{3}-6x^{2}+4x$ The domain of $(f\circ g)(x)$, $(g\circ f)(x)$, $(f\circ f)(x)$ and $(g\circ g)(x)$ are $ R $
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