# Solution: 2018-20 Almost Linear Function

Let $$f:\mathbb R\to\mathbb R$$ be a function such that $-1\le f(x+y)-f(x)-f(y)\le 1$ for all reals $$x$$, $$y$$. Does there exist a constant $$c$$ such that $$\lvert f(x)-cx\rvert \le 1$$ for all reals $$x$$?

The best solution was submitted by Ha, Seokmin (하석민, 수리과학과 2017학번). Congratulations!

Here is his solution of problem 2018-20.

An alternative solution was submitted by 채지석 (수리과학과 2016학번, +3). There were two incorrect submissions.

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