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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Label each of the following statements as either true or false.

Let g : A A and f A A . Then ( f g ) ( a ) = ( g f ) ( a ) for every a in A .

To determine

Whether the statement, ‘Let g:AA and fAA. Then (fg)(a)=(gf)(a) for every a in A’ is true or false.

Explanation

Let the two functions of x are f(x) and g(x) such that,

f(x)=x2 and g(x)=x+1

Then,

(fg)(x)=f(g(x))=f(x+1)=(x+1)2=x2+2x+1 ……(1)

And,

(gf)(x)=g(

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