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 - Page 842: 20


$(f\circ g)(x)=-4x^{3}-4x^{2}+24$ $(g\circ f)(x)=-64x^{3}+16x^{2}-6$

Work Step by Step

$f(x)=-4x$ $;$ $g(x)=x^{3}+x^{2}-6$ $(f\circ g)(x)$ To find $(f\circ g)(x)$, substitute $x$ by $g(x)$ in $f(x)$ and simplify: $(f\circ g)(x)=f(g(x))=-4(x^{3}+x^{2}-6)=-4x^{3}-4x^{2}+24$ $(g\circ f)(x)$ To find $(g\circ f)(x)$, substitute $x$ by $f(x)$ in $g(x)$ and simplify: $(g\circ f)(x)=g(f(x))=(-4x)^{3}+(-4x)^{2}-6=...$ $...=-64x^{3}+16x^{2}-6$
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