Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.4 The Algebra of Functions - 7.4 Exercise Set - Page 476: 25


$(F\cdot G)(a) = -a^3+5a^2+2a-10$

Work Step by Step

RECALL: $(F\cdot G)(x) = F(x) \cdot G(x)$ Using the formula above gives: $(F\cdot G)(x) \\= F(x)\cdot G(x) \\=(x^2-2)\cdot (5-x) \\=x^2(5)-x^2(x)-2(5)-(2(-x)) \\=5x^2-x^3-10+2x \\=-x^3+5x^2+2x-10$ To find $(F\cdot G)(a)$, substitute $a$ to $x$ in the equation above to obtain: $(F\cdot G)(x) = -x^3+5x^2+2x-10 \\(F\cdot G)(a) = -a^3+5a^2+2a-10$
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