College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Review Exercises - Page 279: 103

Answer

$(fg)(x)=3x^4-9x^3-16x^2+12x+16$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To find the expression, $ (fg)(x) ,$ given that \begin{array}{l}\require{cancel} f(x)=3x^2-4 \text{ and } \\g(x)=x^2-3x-4 ,\end{array} use the definition of the appropriate function operation. $\bf{\text{Solution Details:}}$ Using $(fg)(x)=f(x)g(x),$ then \begin{array}{l}\require{cancel} (fg)(x)=(3x^2-4)(x^2-3x-4) \\\\ (fg)(x)=3x^2(x^2)+3x^2(-3x)+3x^2(-4)-4(x^2)-4(-3x)-4(-4) \\\\ (fg)(x)=3x^4-9x^3-12x^2-4x^2+12x+16 \\\\ (fg)(x)=3x^4-9x^3-16x^2+12x+16 .\end{array}
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