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2022 OIM Problems/Problem 3

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Problem

Let $\mathbb{R}$ be the set of real numbers. Find all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying the following conditions simultaneously:

(i) $f(yf(x)) + f(x - 1) = f(x)f(y)$ for every $x, y$ in $\mathbb{R}$.

(ii) $|f(x)| < 2022$ for every $x$ with $0 < x < 1$.

Solution

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See also

https://sites.google.com/uan.edu.co/oim-2022/inicio

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