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Regional Olympiad - FBH 2016 Grade 12 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016

September 22, 2018
functionfunctional equationalgebra

Problem Statement

Find all functions f:Q→Rf : \mathbb{Q} \rightarrow \mathbb{R} such that: a)a) f(1)+2>0f(1)+2>0 b)b) f(x+y)−xf(y)−yf(x)=f(x)f(y)+f(x)+f(y)+xyf(x+y)-xf(y)-yf(x)=f(x)f(y)+f(x)+f(y)+xy, ∀x,y∈Q\forall x,y \in \mathbb{Q} c)c) f(x)=3f(x+1)+2x+5f(x)=3f(x+1)+2x+5, ∀x∈Q\forall x \in \mathbb{Q}
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