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International Zhautykov olympiad 2014 problem 2

Source:

January 14, 2014

functionalgebrafunctional equationalgebra proposed

Problem Statement

Does there exist a function

f: \mathbb R \to \mathbb R

satisfying the following conditions: (i) for each real

y

there is a real

x

such that

f(x)=y

, and (ii)

f(f(x)) = (x - 1)f(x) + 2

for all real

x

?
Proposed by Igor I. Voronovich, Belarus