Problem #PRU-110035

Problems Calculus Functions of one variable. Continuity Certain properties of a function and recurrence relations. Algebra and arithmetic Absolute value Inequalities containing absolute values Trigonometry Trigonometrical inequalities

Problem

Does there exist a function \(f (x)\) defined for all \(x \in \mathbb{R}\) and for all \(x, y \in \mathbb{R}\) satisfying the inequality \(| f (x + y) + \sin x + \sin y | < 2\)?