Domain of a Function Definition

The domain is a set of specific numbers given to a function to get real output. In simple words, we can say that we will add certain values for an independent variable to find the value of a dependent variable.

To understand this, let us first quickly tell you what is a function, independent variable, and dependent variable. .

  • The function is a particular mathematical operation that relates two or more variables.
  • The Independent variable in a function is the one that can change its value independently.
  • The dependent variable is the one that will get particular values by putting certain values of the other variable in the function.

Now, you may have a quick idea about these terminologies. Let us again revise the definition in simple words The domain is the collection of numbers of independent variables on which a function can give real values.

For example,

If you have a function y(x) + 3x - 7, then domain includes all those values by putting which we will get real values for

How to find the domain of a function?

To find the domain of a function is pretty simple, you only have to keep putting the numbers from the given set in the function to check which one is giving real value in the output.

You have to keep collecting all those values in a separate set that are giving real values. The set that you will get at the end of your calculation will show you the Domain of that function.

Do you know?

What will you get for every input as a domain? The result that you will get is called the Range of that function


You can read about Range in detail here

Special Condition of Domain

When finding a Domain, you should keep the following factors in your mind.

  • The denominator can’t be zero. A number that is giving “0” in the denominator will not be included as the domain of that function. 
  • The range you will get for a function with a square root must have a positive value inside the root. If it has a negative value, the number will be considered an invalid Domain.


What is the significance of the Domain?

It has great importance in practical Mathematics that is used in different fields of Engineering. By using this, we can solve many problems related to Discrete Mathematics

Can we show the domain and range in picture format?

Yes, we can show the domain and range of a particular function in pictorial format. It depends on your choice of which type of picture you have to use.