2022 OIM Problems/Problem 3

Problem

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

(i)$ (Error compiling LaTeX. Unknown error_msg)f(yf(x)) + f(x − 1) = f(x)f(y)x, y\mathbb{R}$.

(ii)$ (Error compiling LaTeX. Unknown error_msg)|f(x)| < 2022x0 < x < 1$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

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