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Given f(x + f(y)) = f(x) + y, x, y ∈ R. Find f(1000).

1. 1000
2. 2000
3. 500
4. None of these

Correct answer: 1000

Solution

Using the functional equation f(x + f(y)) = f(x) + y, substituting x = 0 shows that f(f(y)) = y, implying f(x) = x. Thus, f(1000) = 1000.

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