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Find f(18/1991)

Source: Iberoamerican Olympiad 1991

April 28, 2007
functionalgebra proposedalgebra

Problem Statement

Let f: [0, 1]→Rf: \ [0,\ 1] \rightarrow \mathbb{R} be an increasing function satisfying the following conditions: a) f(0)=0f(0)=0; b) f(x3)=f(x)2f\left(\frac{x}{3}\right)=\frac{f(x)}{2}; c) f(1−x)=1−f(x)f(1-x)=1-f(x). Determine f(181991)f\left(\frac{18}{1991}\right).
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