A Cantor-Style Function

★ 6/10functions Monotonicity Functional Equations

Problem

A function $f$ defined on $\mathbb{R}$ satisfies

f(x) + f(1 - x) = 1, \qquad f(x) = 2f\!\left(\frac{x}{5}\right),

and $f(x_1) \leqslant f(x_2)$ whenever $0 \leqslant x_1 \leqslant x_2 \leqslant 1$ . Find

f\!\left(\frac{1}{2022}\right).

Answer

Solution

Difficulty	6/10
Topics	functions, Monotonicity, Functional Equations

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