Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2022 OIM Problems/Problem 3

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

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_OIM_Problems/Problem_3&oldid=207204"