Domain and codomain

[Dr.Peterson]

okay, then what

Ultimately, as far as I'm concerned, the only way to decide how to answer the codomain question is to ask your instructor what the intent of the problem is. You have given two answers, both of which I consider valid. The question itself is not consistent with the definition you quoted, unless there is something else you have been taught about what to assume as the codomain in a function for which no codomain is explicitly stated.

This is true of domains: When no domain is stated, we assume, by default, that it is the largest possible domain subject to contextual requirements (e.g. we assume it is all real numbers for which the expression is defined, when we are working with functions of real numbers). I am not aware of such conventions for the codomain, but you may well have some. (One convention would be to always assume the codomain is R!)

 

[Steven G]

Here is a good example for you.

Suppose the domain X = {0,1,2,3}
and the codomain Y = {-1,0,1,2,3,4,5,6}
Suppose the function f contains the points {(0,2), (1,3), (2, -1), (3,6)}

As defined above, f is a mapping from X to Y, that is f: X->Y.
What is the range of f?

 

[Loki123]

Here is a good example for you.

Suppose the domain X = {0,1,2,3}
and the codomain Y = {-1,0,1,2,3,4,5,6}
Suppose the function f contains the points {(0,2), (1,3), (2, -1), (3,6)}

As defined above, f is a mapping from X to Y, that is f: X->Y.
What is the range of f?

2,3,-1,6

 

[Steven G]

2,3,-1,6

Perfect.

 

[Loki123]

Ultimately, as far as I'm concerned, the only way to decide how to answer the codomain question is to ask your instructor what the intent of the problem is. You have given two answers, both of which I consider valid. The question itself is not consistent with the definition you quoted, unless there is something else you have been taught about what to assume as the codomain in a function for which no codomain is explicitly stated.

This is true of domains: When no domain is stated, we assume, by default, that it is the largest possible domain subject to contextual requirements (e.g. we assume it is all real numbers for which the expression is defined, when we are working with functions of real numbers). I am not aware of such conventions for the codomain, but you may well have some. (One convention would be to always assume the codomain is R!)

i will do that.