MathDB

f (x/y) = f(x) + f(y) - f(x)f(y)

Source: 2015 Saudi Arabia IMO TST I p1

July 24, 2020

algebrafunctionalfunctional equation

Problem Statement

Find all functions

f : R_{>0} \to R

such that

f \left(\frac{x}{y}\right) = f(x) + f(y) - f(x)f(y)

for all

x, y \in R_{>0}

. Here,

R_{>0}

denotes the set of all positive real numbers.
Nguyễn Duy Thái Sơn