JEE Math Practice Question

Let $$f(x)=\left[x^{2}-x\right]+|-x+[x]|$$, where $$x \in \mathbb{R}$$ and $$[t]$$ denotes the greatest integer less than or equal to $$t$$. Then, $$f$$ is :

1. A.continuous at $$x=0$$, but not continuous at $$x=1$$
2. B.continuous at $$x=0$$ and $$x=1$$
3. C.continuous at $$x=1$$, but not continuous at $$x=0$$
4. D.not continuous at $$x=0$$ and $$x=1$$