JEE Main 2022 Mathematics question

Let f : be a continuous function satisfying f(x) + f(x + k) = n, for all x R where k > 0 and n is a positive integer. If and then

Answer: (3)

Solution

Replacing x by x + k gives f(x + k) + f(x + 2k) = n, so f(x + 2k) = f(x), and f has period 2k. Then dx + $f

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Question ID VK-034873