domain and range

Domain and Range

Domain and range are the input and output values of the given function respectively.

In this section we will discuss about domain and range of a function.

Domain – The input values in a given function is called Domain of a function. The values that go into function is called domain.
Example : Determine the domain of the following relations
1. {(1, 2) (1, 4) (1, 6) (1, 8)}
Domain = {1}

2. R = { (1, x) (1, z) (3, x) (4, y)}
Df = {1, 3, 4}

3. { (x, y): x ∈N, y∈N and x+y = 10}
Df = {0,1,2,3,4,5,6,7,8,9}

4. { (x, y): y = |x – 1|, x ∈z and |x| ≤ 3}
Df = {-3, -2, -1, 0, 1, 2, 3}

5. {(x, y)}: x ∈N, x < 5, y = 3}
Df {1, 2, 3, 4}

6) R = { (x = 1, x + 5) : x∈ {0, 1, 2, 3, 4}
Domain = x + 1
For x = 0
x + 1 = 0 + 1 = 1
For x = 1, x + 1 = 2
For x = 2, x + 1 = 3
For x = 3, x + 1 = 4
For x = 4, x + 1 = 5
For x = 5, x + 1 = 6
Df = {1, 2, 3, 4, 5, 6}

Range: Let A and B be two sets. Relation from A into B is a subset of AxB. Let R be a relation from A into B. If (a, b) ∈ R, we say that ‘a’ is related to b with respect to R. the set of all those elements a ∈A. Such that (a, b) ∈R for some b∈B is called the domain of R and Range of R to be the subsets of B = {b∈B (a, b) ∈R for some a∈A} B is called the co-domain of R.
Example 1: Determine the range { (1, 2) (1, 4) (1, 6) (1, 8)}
Solution: Range = {2, 4, 6, 8}

Example 2 : – Determine the range of relation R defined by
R = { (x + 1, x+5): x∈ (0, 1, 2, 3, 4, 5)}
Solution: Rf= x + 5
For x = 1, 1 + 5 = 6
For x = 2, 2 + 5 = 7
For x = 3, 3 + 5 = 8
For x = 4, 4 + 5 = 9
For x = 5, 5 + 5 = 10
So, Rf = {5, 6, 7, 8, 9, 10}

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