Suppose f:R→Rf: \mathbb{R} \to \mathbb{R}f:R→R satisfies ∣f(x)−f(y)∣≤∣sin(x)−sin(y)∣|f(x) - f(y)| \leq |\sin(x) - \sin(y)|∣f(x)−f(y)∣≤∣sin(x)−sin(y)∣. What can be concluded about fff?
fff is constant.
fff is Lipschitz continuous.
fff is differentiable everywhere.
fff must be a periodic function with period 2π2\pi2π.