## About "How to find domain of a function"

How to find domain of a function ?

Here we are going to see how to find domain of a function.

What is domain ?

The domain of a function is the complete set of possible values of the independent variable.

In other words, the domain of f(x) is the set of all those real numbers for which f(x) is meaningful.

For example, let us consider the function

f(x)  =  (3x - 2)/(x2 - 1)

The above function accepts all real values except -1 and 1.If we apply x = 1 and -1, the function will become meaningless.

Hence the domain of the given function is R - {-1, 1}

Let us look into some example problems to understand the above concept.

Example 1 :

Find the domain of the following function

f(x)  =  1 / (x + 2)

Solution :

The given function accepts all real values except -2. In the given function if we apply -2 instead of x, it will become undefined.

Hence the domain of f(x) is R - {-2}

Example 2 :

Find the domain of the following function

f(x)  =  (x - 1) / (x - 2)

Solution :

In numerator, we don't have any restriction for x values. But in the denominator, if we apply x = 2 the function will become undefined.

Hence the domain of f(x) is R - {2}

Example 3 :

Find the domain of the following function

f(x)  =  (2x - 3) / (x2 - 3x + 2)

Solution :

Since we have quadratic equation in the denominator, let us find factors.

x2 - 3x + 2  =  (x - 1) (x - 2)

f(x)  =  (2x - 3) / (x - 1) (x - 2)

In numerator, we don't have any restriction for x values. But in the denominator, if we apply x = 2 or x = 1 the function will become undefined.

Hence the domain of f(x) is R - {1, 2}

Example 4 :

Find the domain of the following function

f(x)  =  (x2 + 3x + 5)/(x2- 5x + 4)

Solution :

We could not find linear factors of the quadratic equation which is in the numerator.

x2- 5x + 4  =  (x - 1) (x - 4)

f(x)  =  (x2 + 3x + 5)/(x - 1) (x - 4)

In numerator, we don't have any restriction for x values. But in the denominator, if we apply x = 1 or x = 4 the function will become undefined.

Hence the domain of f(x) is R - {1, 4}

Example 5 :

Find the domain of the following function

f(x)  =  (2x + 1)/(x2  - 9)

Solution :

f(x)  =  (2x + 1)/(x2  - 32)

By comparing the denominator x2  - 32 with the algebraic identity a2  - b2, we get two factors (x + 3) (x - 3)

f(x)  =  (2x + 1)/(x + 3) (x - 3)

In numerator, we don't have any restriction for x values. But in the denominator, if we apply x = -3 or x = 3 the function will become undefined.

Hence the domain of f(x) is R - {-3, 3}

After having gone through the stuff given above, we hope that the students would have understood "How to find domain of a function".

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