Problem #PRU-110035

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

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 \(| f (x + y) + \sin x + \sin y | < 2\)?