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No function f,g

Source: Iranian third round -Algebra exam 2015 (problem2)

September 8, 2015
functionalgebra

Problem Statement

Prove that there are no functions f,g:R→Rf,g:\mathbb{R}\rightarrow \mathbb{R} such that ∀x,y∈R:\forall x,y\in \mathbb{R}: f(x2+g(y))−f(x2)+g(y)−g(x)≤2y f(x^2+g(y)) -f(x^2)+g(y)-g(x) \leq 2y and f(x)≥x2f(x)\geq x^2. Proposed by Mohammad Ahmadi
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