Limit of function defined as $|f(x)-f(y)|<K|x-y|$

Question

I'm looking for a hint on how to solve the following problem:

if $f$ is a function satisfying the following property: There exists a constant $K\in\mathbb{R}$ such that $|f(x)-f(y)|\le K|x-y|$ for all $x,y\in \mathbb{R}$ and knowing that $f(2)=7$, then what is $\lim_{x\rightarrow2 }f(x)$?

Answer 1

The function $f$ is $K$-Lipschitz, so it's continuous.

$$\lim_{x\to 2}f(x) = f(2) = 7$$