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Question

If f1(x) and f2(x) are defined on domains D1 and D2 respectively, then f1(x)+f2(x) is defined on D1D2. True or false?
If true enter 1 else 0.

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Solution

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 xϵD1D2.
Consider the possibility that it is defined in the domain D1D2
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 D1D2

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