   Chapter 1.3, Problem 3E

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Textbook Problem
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# Let A = { − 1 ,     0 ,     1 } . Find mappings f : A → A and g : A → A such that f ∘ g ≠ g ∘ f .

To determine

The mappings f:AA and g:AA such that fggf

Explanation

Given information:

A={1,0,1}

Formula used:

Definition: Let g:AB and f:BC. The composite mapping fg is the mapping from A to C defined by (fg)(x)=f(g(x)) for all xA.

Explanation:

Let A={1,0,1}

f:AA and g:AA

Let f(x)=x2,g(x)=x

By using the definition of a composite function,

(fg)(x)=<

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