Question

3. If a function maps Set A to Set B, do all elements of Set A
have to be used?

Answer 1

If it’s maps all of its domains

Answer 2

So we have a function such that:

Takes elements of Set A, and maps them into Set B.

So Set A is the domain, and Set B is the range.

Where the domain is defined as the set of all the possible inputs of a function, and the range is the set of the possible outputs.

In principle, yes, if f(x) maps Set A into Set B, all the elements of Set A should be used, why?

Because we need to check if there is a problem with Set A, for example the function f(x) = 1/x has a problem when x = 0, so we remove x = 0 from the domain of that function.

So, a function is only a function if it maps ALL the elements of its domain into only one element in the range.