Get domain of a function over the reals

[Kreijstal]

is it possible after sets being developed to get the domain over the reals of an arbitrary function? I was thinking about different algorithms to implement such function, I will try to explain in pseudocode how it could work out: a similar algorithm can be used to find the domain of a function over the complex numbers

for any given function if f(x)=k*g(x) the domain over the reals of f(x) is the domain of g(x) if f(x)=g(x)+h(x) the domain over the reals of f(x) is the domain of g(x) ∩ h(x) if f(x)=g(x)+c the domain over the reals of f(x) is the domain of g(x) if f(x)=g(x)*h(x) the domain over the reals of f(x) is the domain of g(x) ∩ h(x) if f(x)=1/g(x) the domain over the reals of f(x) is the set solution to g(x)≠0 In this case because we assume that division is undefined over zero.

I wanted to be general with exponentials, but it seems that cubic roots might have different intepretations, https://www.intmath.com/blog/mathematics/is-cube-root-the-same-as-raising-to-power-13-10460 , so I don't know how to interpret it.

[Happypig375]

Related to Section 5.2 of #350

[jiggzson]

@Kreijstal thanks for the proposal. Looking at this proposal it seems that the way to implement this is would be by using a lookup table for functions. Do you know of a way to accomplish this arithmetically?

[dhiahassen]

@jiggzson check sympy's way of doing it https://stackoverflow.com/questions/55881078/how-to-know-whether-a-function-is-continuous-with-sympy/55885282#55885282

you can read it's code