Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.1 - The Algebra of Functions - Exercise Set: 19

Answer

$(f\circ g)(x)=-8x^{3}-2x-2$ $(g\circ f)(x)=-2x^{3}-2x+4$

Work Step by Step

$f(x)=x^{3}+x-2;$ $g(x)=-2x$ $(f\circ g)(x)$ To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify: $(f\circ g)(x)=f(g(x))=(-2x)^{3}-2x-2=...$ $...=-8x^{3}-2x-2$ $(g\circ f)(x)$ To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify: $(g\circ f)(x)=g(f(x))=-2(x^{3}+x-2)=-2x^{3}-2x+4$
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