Question

In surjective and injective functions is it possible for elements of the domain not to be mapped to an element of the range? If it is I have further questions. but as an example,


`( (x-1)(x-2)(x-3)(x-4))/(x - 2)`
would have a hole at 2 but still have a value at every y value. so would it be surjective?

Answer 1

Explanation:

The definition of a function f from A to B, regardless to injectivity or surjectivity, is that the domain of f is A, in its entirety.

This means that if f:A→B, then for every a∈A, there is a unique b∈B such that the pair (a,b)∈f.

So the converse holds just for it to be a function from A to B.