IOM 2020, Блиц — Задача 77

The Blitz-contest of IOM-2020

Условие

Calculate $f^{2020}(2020)$, where function $f\colon \mathbb{R} \to \mathbb{R}$ satisfies

$(x - 1) \cdot f(x) + f\left(\frac{1}{x}\right) = \frac{1}{x-1}$

for all real $x \ne 0, 1$.

(Here $f^{2020}$ denotes the $2020$th application of $f$, i.e., $\underbrace{f(f(\dots(f(x))\dots))}_{2020}$, not numerical power.)

Fractional numbers can be entered either as a decimal fraction or as $m/n$.

Отговори

Решение

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Оригинал в Архива: iom-2020-blitz-tasks.pdf · официални решения: iom-2020-blitz-answers.pdf