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# What is the difference between range and codomain?

Updated: 12/24/2022

OneWeirdDude

Lvl 1
12y ago

Sometimes it is useful to distinguish between the set of images of the domain of a function, which is called the RANGE of the function, from the super-set of the range. For example, for the real function x^2 without any additional qualification, its domain is the set of real numbers and its range is the non-negative reals. The codomain is the entire set of reals that the non-negative reals are part of. So the codomain is the super-set of the range. Curiously, there is no corresponding term for the domain, which might be called the "co-range" but we have no single word for it. If we did, it would simply mean the entire set of which the domain is a subset. So, for example, the domain of the real (otherwise unrestricted) square root of x is the set of non-negative reals and its co-range, if we spoke of it, would be the entire set of reals. We can think of these as the difference between a family and a subset of individuals.

Wiki User

12y ago

Wiki User

12y ago

Range of a function f, is the set of attainable points IN the co-domain that f maps elements to.

Co-domain is the space in which the mapped-to elements live.

For example:

say f:R -> R (f maps real numbers to real numbers)

such that

f (t) = e^t

It is true that the co-domain is all real numbers, yet the range is the set of all POSITIVE real numbers, not all the real numbers.

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Related questions

### What is the set of y-values?

It is the codomain or range.

### What are possible values for y called?

They comprise the codomain or range.

### Which term describes the set of all possible values in a function?

The codomain or range.

### What is the set of all output values of a relation?

It is the codomain, often called the range.

### What scale would be appropriate to make a graph of the data?

It depends on the domain and codomain (range) of he data.

### What is the domain of square root of x square minus six?

Within reason, it can be anything. The answer depends on what you want the codomain (range) to be.If the codomain is to be integers, the domain must be {x | x = n2 -2n + 7 where n is in N}If the codomain is to be the real numbers, the domain must be {x | x is in R, x2 &acirc;&permil;&yen; 6},If the codomain is the set of complex numbers, then the domain is R.There is a more complicated answer if the codomain is to be the set of rational numbers.But, essentially, the answer is "it depends".

### What is the codomain?

The codomain of a function is an arbitrary set that contains all the images of a function. Thus, the function defined by f(x) = cos x + i sin x might be said to have codomain C, or the set of all complex numbers. The range is much more specific: it is the set of all the images, and nothing more. In this case, the range is {a + bi = z in C: |z| = 1}.

### What are some function words?

Domain, codomain, range, surjective, bijective, invertible, monotonic, continuous, differentiable.

### What is a set of all output values of a relation?

It is known as the codomain, although the term range is also used.

### What is the difference between range rover hse and hst?

difference between Range Rover HSE / HST

### How does the domain relate to a function?

Any function is a mapping from a domain to a codomain or range. Each element of the domain is mapped on to a unique element in the range by the function.

### How do you determined if a relation is a function?

For every element on the domain, the relationship must allocate a unique element in the codomain (range). Many elements in the domain can be mapped to the same element in the codomain but not the other way around. Such a relationship is a function.