Let the function $$f$$ be defined on the set of real numbers by 

$$ f(x) = \begin{cases}x^2 - x, & if x < 1\\\frac{x^2 - 1}{3}, &if x \geq 1\end{cases}$$ then which of the following statement is TRUE ?

A

$$f$$ is decreasing for $$x<1$$ and increasing for $$x \geq 1$$

B

$$f$$ is not continuous at $$x = 1$$

C

$$f$$ is continuous but not differentiable at $$x =1$$

D

$$f$$ is differentiable at $$x = 1$$