# Range and Domain

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Domain and range is a very important concept in functions. Domain of a function is all the input values that can be assigned to the function's variable which defines the value of the function. Let y = f(x) be a function. So domain for a function f(x) domain of the function are all the possible input values of X. The range of the function is all the value which are derived using f(x) or all the possible values of y.

Example 1: Find the domain of the function f(x) = 3 x/ [(x - 2) (x- 5)?

Solution: Given is a function f(x) = 3x/ [(x- 2) (x- 5)];

The domain of the function is all the possible input values of X.

First step: Equate the dominator [(x - 2) (x- 3)] = 0

This gives the values x = 2 and x = 3;

Hence when x = 2, 3 the function is undefined as denominator = 0;

Therefore the domain of the function is: R - {2 ,3}

Example 2: Find the domain of the function f(x) = 10 x/ [(x + 6) (x- 12)]?

Given is a function f(x) = 10x/ [(x + 6) (x- 12)];

The domain of the function is all the possible input values of X.

First step: Equate the dominator [(x + 6) (x- 12)] = 0

This gives the values x = -6 and x = 12;

Hence when x = -6, 12 the function is undefined as denominator = 0;

Therefore the domain of the function is:  R - {-6 ,12}