Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 7 - Functions - Exercise Set 7.1 - Page 394: 16

Answer

$(F-G)(x)=F(x)-G(x)\,\,\,\,\,\,by\,definition\,of\,(F-G)(x)\\ (F-G)(x)=F(x)-G(x)=-(G(x)-F(x))=-(G-F)(x)\\ by\,definition\,of\,(G-F)(x)\\ \because (F-G)(x)=-(G-F)(x)\\ \therefore F-G\neq G-F\\ $

Work Step by Step

$(F-G)(x)=F(x)-G(x)\,\,\,\,\,\,by\,definition\,of\,(F-G)(x)\\ (F-G)(x)=F(x)-G(x)=-(G(x)-F(x))=-(G-F)(x)\\ by\,definition\,of\,(G-F)(x)\\ \because (F-G)(x)=-(G-F)(x)\\ \therefore F-G\neq G-F\\ $
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