Let f(x) = nx + n - [nx+n] + x 2 , where [x] is the greatest integer x and n N. It is

JEE Advanced Mathematics question

Let , where is the greatest integer and . It is

(A)a periodic function of period
(B)a periodic function of period
(C)not periodic
(D)a periodic function of period Correct

Answer: (D)

Solution

, because is an integer. The fractional part has period 1, so has (fundamental) period . Its periods are , and they include and . has period . The LCM of and is , so

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Question ID VK-109171