Let r be a real number and $$f(x) = \begin{cases}2x -r & ifx \geq r\\ r &ifx < r\end{cases}$$. Then, the equation $$f(x) = f(f(x))$$ holds for all real values of $$x$$ where

A

$$x > r$$

B

$$x \leq r$$

C

$$x \neq r$$

D

$$x \geq r$$