MathDB

f(x+y)=\frac{f(x)+f(y)}{1+f(x)f(y)} (VI Soros Olympiad 1990-00 R2 10.3)

Source:

May 28, 2024

algebrafunctional equationfunctional

Problem Statement

Find all functions

f

that map the set of real numbers into the set of real numbers, satisfying the following conditions:
1)

|f(x)|\ge 1

,
2)

f(x+y)=\frac{f(x)+f(y)}{1+f(x)f(y)}

of all real values of

x

and

y