NTA Abhyas JEE Main2020MathematicsFunctionsPractice

Let f : R → R be a periodic function such that f T + x = 1 + 1 - 3 f x + 3 f x 2 - f x 3 1 3 where T is a fixed positive number, then period of f x is

Options

AT
B2 T
C3 T
DNone of these

Correct answer

B. 2 T

Step-by-step solution

Given : f T + x = 1 + 1 - f x 3 1 3 = 1 + 1 - f x ⇒ f T + x + f x = 2 ... (1) ⇒ f 2 T + x + f T + x = 2 ... (2) Subtracting (1) from (2) f 2 T + x - f x = 0 f 2 T + x - f x = 0 Also, T is positive therefore period of f x = 2 T

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