# 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}