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f(f(x)) = bx f(x) +a, where f surjective

Source: 2015 Belarus TST 3.1

November 5, 2020
functional equationalgebrafunctional

Problem Statement

Do there exist numbers a,b∈Ra,b \in R and surjective function f:R→Rf: R \to R such that f(f(x))=bxf(x)+af(f(x)) = bx f(x) +a for all real xx?
I.Voronovich
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