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Black Book Advanced Problems in MathematicsMathematicsFunctions

Let f(x) be a real valued continuous function such that f(0) = 1 2 and f(x + y) = f(x)f(a - y) + f(y)f(a - x) x, y R , then for some real a :

Options

  1. Af(x) is a periodic function
  2. Bf(x) is a constant function
  3. Cf(x) = 1 2
  4. Df(x) = x 2

Correct answer

A. f(x) is a periodic function

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