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Possible values of f(2018)

High school · ●●●○○ 50 pts

Let f:Z→Zf: \mathbb{Z} \rightarrow \mathbb{Z} be an even function with f(1)=1f(1)=1 and f(2017)≠1f(2017) \neq 1. For all integers x,yx, y, 2f(x+y)−f(x)−f(y)⩽∣f(x)−f(y)∣2f(x+y)-f(x)-f(y) \leqslant |f(x)-f(y)|. Find the value of f(2018)f(2018).

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functional inequalitieseven functionsinduction