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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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For the given subsets A and B of Z, let f ( x ) = | x + 4 | and determine whether f : A B is onto and whether it is one-to-one. Justify all negative answers.

a. A = Z , B = Z b. A = Z + , B = Z +

a)

To determine

Whether the mapping f:AB is one-to-one or onto or both.

Explanation

Given Information:

The given function is,

f(x)=|x+4|

The subset of A is Z and the subset of B is Z.

Explanation:

Let f:XY

Function f is called one-to-one, if and only if different elements of A always have different images under f.

Function f is called onto if and only if f(x)=y.

Consider the given function,

f(x)=|x+4|

Let 9 and 1 are elements in A.

Then,

f(9)=f(1)|9+4|=|1

b)

To determine

Whether the mapping f:AB is one-to-one or onto or both.

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