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

f(x) Is discontinuous at some x

f(x) Is continuous at all x, but the derivative f¹(x) does not exist for some x

f¹(x) exists for all x

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