Difference between Codomain and Range

Can the range and the codomain be the same?

Yes, the range and the codomain can be the same if the function maps to every element of the codomain. This happens in cases where the function is surjective (onto).

Is it possible for a function to have an empty range?

No, a function must have at least one output for every input in its domain, as the range cannot be empty.

Can the codomain be smaller than the range?

No, the codomain cannot be smaller than the range. The codomain is always at least as large as the range since the range is a subset of the codomain.

How to differentiate between range and codomain?

Codomain defines all possible output values, whereas the range consists only of the actual output values attained by the function.

How do you determine the range of a function?

To determine the range, you need to apply the function to all possible inputs in the domain and collect all unique outputs.

Why is the distinction between codomain and range important?

The distinction is important for understanding the properties of functions, such as injectivity and surjectivity, and for correctly applying mathematical concepts in various fields.

Codomain is the set that contains all possible values that the function can output, Range of a function, on the other hand, is the set of all output values that are actually attained by the function. Although they might seem similar initially, but they have different meanings and uses.

This article will explain the meaning of co-domain and range of a function along with the difference between codomain and range.