MathDB

10

Part of 1995 Baltic Way

Problems(1)

Find all f

Source: Baltic Way 1995

10/8/2011
Find all real-valued functions ff defined on the set of all non-zero real numbers such that:
(i) f(1)=1f(1)=1, (ii) f(1x+y)=f(1x)+f(1y)f\left(\frac{1}{x+y}\right)=f\left(\frac{1}{x}\right)+f\left(\frac{1}{y}\right) for all non-zero x,y,x+yx,y,x+y, (iii) (x+y)⋅f(x+y)=xy⋅f(x)⋅f(y)(x+y)\cdot f(x+y)=xy\cdot f(x)\cdot f(y) for all non-zero x,y,x+yx,y,x+y.
functionalgebrafunctional equationalgebra proposed