Can the codomain of a function not include image points that are in the range. For instance, f: R--- [0,Infinity) where f(x)==x. See the codomain is only from 0 to infinity, but the range can include -1 for example and other negative numbers. So I guess this means the range is bigger than the codomain. Can that ever happen? If so, why can it happen??????

Question

Can the codomain of a function not include image points that are in the range. For instance, f: R---> [0,Infinity) where f(x)==x. See the codomain is only from 0 to infinity, but the range can include -1 for example and other negative numbers. So I guess this means the range is bigger than the codomain. Can that ever happen? If so, why can it happen??????

anonymous · Answer

No.  The range of a function is a subset of its codomain.