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|f(x + y) + sinx + siny| < 2 - All-Russian MO 2000 Regional (R4) 10.5

Source:

September 26, 2024
algebrainequalitiesfunctionfunctionaltrigonometry

Problem Statement

Is there a function f(x)f(x) defined for all x∈Rx \in R and for all x,y∈Rx, y \in R satisfying the inequality ∣f(x+y)+sin⁡x+sin⁡y∣<2?|f(x + y) + \sin x + \sin y| < 2?
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