# 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}

12th grade math

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