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Domain and RangeDomain 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 codomain 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 From Domain and range to Home
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