A removable singularity should not count for the domain. I understand that the domain of f(x) is the set of x for which the calculations indicated in the formula for f(x) lead to a numerical value, say real or complex. The domain of x^2/x
does not include 0
.
In my view, FunctionDomain
lets the system make some algebraic simplifications that do not always preserve the domain. From the point of view of algebra, p(x)/q(x)=a(x)/b(x)
if p(x)b(x)=a(x)q(x)
, where a,b,p,q
are polynomials. In this sense x^2/x=x/1=x
. But q
and b
can have different zero sets, and p/q
and a/b
can have different domains. For abstract algebra, a rational function is not really a point function.