Math Is Fun Forum

Cartis

Guest

Function

Can you define codomain of a function like dom(f),ran(f)?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Function

hi Cartis,

Welcome to the forum.

Can you define codomain of a function like dom(f),ran(f)?

What are these functions please?  I cannot find either in a maths dictionary.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Cartis

Guest

Re: Function

I am sorry,I meant dom(f(x)),domain of f(x),and ran(f(x)),range of f(x)

noelevans

Member

Registered: 2012-07-20

Posts: 236

Re: Function

Hi Cartis!

The codomain of a function from X into Y is Y.  The range of the function is the subset of Y consisting
of all the elements of Y that are actually paired with an element of X via the function.
The domain of the function can be thought of as all the INPUTS to the function and the range as all
the OUTPUTS.

---

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Function

hi Cartis,

I've made a drawing below which may make this clearer.

When a function is defined the definition should include saying what set the function may be applied to.  This set is called the domain.

It should also include a statement of what set the function maps to.  This second set is called the codomain.

But some elements of the codomain may not be mapped onto.  So the word range is used for the subset of the codomain that actually gets mapped to.

I'll make up an example.

Domain = {counting numbers} Codomain = {counting numbers}  Fuinction f(x) : x ---> 5x

For this function the Range = {5,10,15,20,25,.......}

Other members of the codomain such as 3, 17, 29 etc are not mapped to by f.

The definition of the domain is important. 

If I change the domain and codomain in the above example both to {real numbers} then every member of the codomain is mapped to (since we can always take an element, y,  of the codomaiin, divide it by 5, and that answer (y/5) is the member of the domain that maps onto y.

Thus {range} = {codomain}

[I have seen a number of questions posted where the student is asked to say what the domain is for a particular function.  I consider this unreasonable since the domain is part of the definition and many answers are possible and equally valid.] 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob