A Self-Similar Function

★ 7/10functions Monotonicity Functional Equations

Problem

A function $f$ on $\mathbb{R}$ satisfies $f(0) = 0$ ,

f(x) + f(1-x) = 1, \qquad f\left(\frac{x}{5}\right) = \frac12 f(x),

and $f$ is nondecreasing on $[0, 1]$ . Find

f\left(\frac{1}{2015}\right).

Answer

Solution

Difficulty	7/10
Topics	functions, Monotonicity, Functional Equations

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