FunctionDomain

FunctionDomain[f,x] finds the largest domain of definition of the real function f of the variable x. 

FunctionDomain[f,x,dom] considers f to be a function with arguments and values in the domain dom.

FunctionDomain[funs,vars,dom] finds the largest domain of definition of the mapping funs of the variables vars. 

FunctionDomain[{funs,cons},vars,dom] finds the domain of funs with the values of vars restricted by constraints cons.

Please visit the official Wolfram Language Reference for more details and examples on core symbols.