# Definition Of Domain In Math

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Domain is set of values of independent variable for which a function is defined. In simple words, Domain is the set of input values given to a function.  The domain of a function is the set of input values which allows the function to work. Mostly domain is the set of all real numbers.  In a relation, domain is a set of x coordinate of the ordered pair of that relation. For example, in a relation (3, 4), (9, 7), (12, 15) the domain of the relation is 3, 9 and 12.

Example 1: (-4, 2) (2,-8) (5,-7) (8,-10). What is the domain of the set of ordered pairs given?

Solution: The domain of a set of ordered pairs is the set of x-coordinates.
In this set of ordered pairs, the x-coordinates are -4, 2, 5, and 8.
Therefore the domain is {-4, 2, 5, 8}

Example 2: Given the range {-1, -2, 2}, what is the domain for the relation y = x - 3?

Solution: First, rewrite the equation in terms of x.
y = x – 3
y + 3 = x -3 + 3
x = y + 3
Next, substitute range values in for y in the equation x = y + 3.
When y = -1 then x = -1 + 3 = 2
Similarly when y = -2 then x = 1
When y = 2 then x = 5
Therefore, the domain is {2, 1, 5}.