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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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  1. Find mappings f , g and h of a set A into itself such that f g = h g and f h .

  2. Find mappings f , g and h of a set A into itself such that f g = f h and g h .

(a)

To determine

The mappings of f,g and h of a set A into itself such that fg=hg and fh.

Explanation

Let f,g and h be the mappings of set of integers A=Z into itself defined as,

f(x)=x, g(x)=x2 and h(x)=|x|, for all xZ.

Then,

(fg)(x)=f(g(x))=f(x2)=x2

And,

(hg)(x)=h(g<

(b)

To determine

The mappings of functions f,g and h of a set A into the set A itself such that fg=fh and gh.

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