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Inequality over functions

Source: Iran 3rd round 2009 - final exam problem 4

January 2, 2015
inequalitiesfunctionalgebra unsolvedalgebra

Problem Statement

Does there exists two functions f,g:R→Rf,g :\mathbb{R}\rightarrow \mathbb{R} such that: ∀x≠y:∣f(x)−f(y)∣+∣g(x)−g(y)∣>1\forall x\not =y : |f(x)-f(y)|+|g(x)-g(y)|>1
Time allowed for this problem was 75 minutes.
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