question_answer

For a real number y, [y] denotes the greatest integer less than or equal to y, then ,   tan \[f(x)=\frac{\tan \left( \pi \left[ x-\pi  \right] \right)}{1+{{\left[ x \right]}^{2}}}\]is

A)  Discontinuous at some x   

B)  Continuous at all x, but \[f'(x)\] does not exist for some x

C)  \[f'(x)\]exists for all x but  \[f''(x)\]does not exist 

D)  \[f'(x)\]exists for all x