IMO 1989 LL FIN17

Let a, 0 < a < 1, be a real number and f a continuous function

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IMO 1989 LL FIN17

Origin: FIN

Problem

Let a, 0 < a < 1, be a real number and f a continuous function on [0, 1] satisfying f(0) = 0, f(1) = 1, and f x + y  = (1 −a)f(x) + af(y) for all x, y \in[0, 1] with x \leqy. Determine f(1/7).