Domain Calculator

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Domain of a function is the set of all possible values of the independent variable (generally represented by ‘x’) so that the given function exists. For many functions the domain is the set of all real numbers, however there are also many functions where there are certain limitations on the ‘x’ values. Domain calculator is the fun tool which can instantly give the domain of any function.


Example 1: Find the domain of the function, f(x) = 1/x.

Given function, f(x) = 1/(x)

Here we have an expression in the denominator.

Domain is the set of values of ‘x’ for which the function f(x) exists!

We know that if there is ‘0’ in the denominator, then the value is undefined.
1/0 = undefined

If x = 0, then the function value f(x) = undefined and does not exist!
x ≠ 0

Hence the domain of the function is any Real number, R except ‘0’.

Domain = R – {0}


Example 2: Find the domain of the function, f(x) = 1/√x.

Here we have a square root expression in the denominator and hence we have 2 limitations:

1) We know that if there is ‘0’ in the denominator, then the value is undefined.

1/0 = undefined     Hence x ≠ 0

2) We know that inside any square root, there can never be a negative number.

‘x’ can be any positive number, but ‘x’ cannot be any negative number.

Hence the domain of function does not include negative numbers and ‘0’.

Domain > x > 0

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