If f1(x) is defined in the domain of xϵD1 and f2(x) is defined in the domain of xϵD2 then f1(x)+f2(x) is defined in the domain xϵD1∩D2.
Consider the possibility that it is defined in the domain D1∪D2
Then for any element in D1, f2(x) won't be defined. Similarly for any element in D2, f1(x) won't be defined. Hence the above statement is false.
Thus the correct answer is D1∩D2