The function f(x) = x - [x] + x, where [x] = the greatest integer less than or equal to x, is a

JEE Advanced Mathematics question

The function , where = the greatest integer less than or equal to , is a

Answer: (C)

has period 1 and has period . Because is irrational, they have no common multiple.

A rigorous argument: is discontinuous exactly at the integers, because jumps there and is continuous. If were a

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Question ID VK-109170