# Domain of a Function Calculator

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Domain of a function is the set of all possible input values for which the function is valid. The input values are taken for the independent variable in the function usually represented by ‘x’. Domain of a function calculator is the instant online tool which is useful in finding domain for any given function.

Example 1: Find the domain of the function, f(x) = x2 – 4.

Given function, f(x) = x2 – 4

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

If x= 0 > f(0) = 02 – 4 > f(0)= -4 > Valid function value!

Now let ‘x’ be any negative number > x= -2 > then f(-2)= 0

‘x’ is valid for any negative number.

Similarly let ‘x’ be any positive number  > x =1  > then f(1)= -3

’x’ is valid for any positive number as well.

Hence domain of f(x)= x2 - 4 is all Real numbers.

Example 2: Find the domain of the function, f(x) = 1/ (x2 – 5x + 6).

Given function, f(x) = 1/ (x2 – 5x + 6)

Here we have an expression in the denominator.

We know that if there is ‘0’ in the denominator > 1/0 = undefined

We can factor the quadratic expression > (x2 – 5x + 6) = (x – 2)(x – 3)

If x – 2=0 or x – 3=0, then the function value f(x) = undefined!

Hence x–2≠ 0 >  x≠ 2 and similarly x≠ 3

Domain= R – {2, 3}