   Chapter 1.2, Problem 2E

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# For each of the following mapping, state the domain, the codomain, and the range, where f : E → Z . f ( x ) = x 2 ,   x ∈ E f ( x ) = x ,   x ∈ E f ( x ) = | x | ,   x ∈ E f ( x ) = x + 1 ,   x ∈ E

(a)

To determine

The domain, the codomain, and the range of mapping, f:EZ which is defined as f(x)=x2,xE.

Explanation

Formula Used:

Let f be a mapping from A to B. The set A is called the domain of f and B is called codomain of f, Now, The range of f is the set,

And, the range of f is defined by f(A).

Explanation:

Here, we have,

f:EZ.

where, E is the set of even integers including 0, Z is the set of integers and

f(x)=x2forxE

(b)

To determine

The domain, the codomain, and the range of mapping, f:EZ which is defined as f(x)=x,xE.

(c)

To determine

The domain, the codomain, and the range of mapping, f:EZ which is defined as f(x)=|x|,xE.

(d)

To determine

The domain, the codomain, and the range of mapping, f:EZ which is defined as f(x)=x+1,xE.

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