Difference Between Codomain and Range


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Difference Between Codomain and Range

The difference between codomain and range is a bit difficult to find out, because both the terms sometimes means the same. But still, we can slightly differentiate between range and codomain.

The codomain is the set of all possible values which can come out as a result but the range is the set of values which actually comes out. Also, learn relation of domain and range here.

What is the Difference between Codomain and Range?

Codomain is simply the set of values that includes range along with a set of additional values. Understanding the different definitions is important as it helps to clarify the differences between one and the other.

Usually, Codomain and Range serve the same purpose when it comes to figuring out the output of the function. Using a Domain and Range calculator, one can easily find out the solutions to any problems presented to them.

Difference between Codomain and Range
Codomain Range
It is referred to as the range of function along with a few additional values. It is defined as the subset of the codomain
It restricts the output of a function It is totally ambiguous and can be used exactly as Codomain
It refers to the possible set of values, that might come out of it. It refers to the actual, definitive set of values that might come out of it.
It refers to the definition of a function. It refers to the image of a function.

Solved Example

Let us consider a function, f(a) = 2a

Now for each value of a, we will get different output for function f(a), such that:

If a = 1, then f(a) = 2(1) = 2

If a = 2, then f(2) = 2(2) = 4

If a = 3, then f(3) = 2(3) = 6

Hence, if the input is given 1 then the output will be 2, so 1 is the domain and 2 is the range for that domain.

But the collection of outputs i.e. (2,4,6) are the codomains of the function.

Thus, this is what is defined as the major difference between Codomain and Range. It is important to know these differences, as they help one define the exact range and set of values. To know more about math-related topics like this, download the BYJU’s app today!

Frequently Asked Questions on the Difference between Codomain and Range

How to differentiate between range and codomain?

The difference between range and codomain is a minute one but an important one. Both represent output but the range is actual output but codomain is the set of possible outcomes.

What is the difference between range and domain?

The domain and range of a function are input and output respectively. The set which contains all the first elements of all the ordered pairs of relation R is known as the domain of the relation. The set which contains all the second elements on the other hand, is known as the range of the relation.

What is image and preimage of a relation?

The preimage and image are nothing but the domain and range of a relation, respectively.

What is codomain in function?

The set of destination of a function is the codomain where all the output of the function is collected, when the function is mapped from domain (input) to the codomain (also called image).