Great!!! Thanks for this post that made me review the theory of functions, I had forgotten some terms. so I also reviewed the concept of domain. I had forgotten that the domain of a function is precisely the set of all input values (i.e. the x) for which the function is defined, i.e. for which it makes sense to calculate the output (i.e. the y or f(x)). It is impossible to remember everything!
RE: Domain and path of a function