Domain and Range of a Function Calculator

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Domain is the set of numbers of the independent variable (‘x’ values) for which the function exists or is valid. Range is the set of appropriate numbers of the dependent variable (‘y’ values). Domain and range calculator is the online tool which can give domain and range vales of a function.


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

Given function, f(x) = 1/(x – 2)

Here we have an expression in the denominator.

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

1/0 = undefined

If x – 2 = 0, then the function value f(x) = undefined and does not exist!
Hence x – 2 ≠ 0    x ≠ 2

Hence the domain of the function is any Real number, R except ‘2’.

Domain = R – {2}



Example 2: Find the range of the above function, f(x) = 1/(x – 2)

Given function, f(x) = 1/(x – 2)

Considering the domain of the function as all real numbers except ‘2’, now let’s look at the statement è 1/(x-2) = 0

Since there is no ‘x’ term in the numerator, the above given statement can never be true! f(x) ≠ 0

Hence the Range of this function is all Real numbers, R except ‘0’.

Range = R – {0}


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