JEE Math Practice Question

Let $$\alpha$$ $$\in$$ R be such that the function $$f(x) = \left\{ {\begin{matrix} {{{{{\cos }^{ - 1}}(1 - {{\{ x\} }^2}){{\sin }^{ - 1}}(1 - \{ x\} )} \over {\{ x\} - {{\{ x\} }^3}}},} & {x \ne 0} \\ {\alpha ,} & {x = 0} \\ \end{matrix} } \right.$$ is continuous at x = 0, where {x} = x $$-$$ [ x ] is the greatest integer less than or equal to x. Then :

1. A.no such $$\alpha$$ exists
2. B.$$\alpha$$ = 0
3. C.$$\alpha$$ = $${\pi \over 4}$$
4. D.$$\alpha$$ = $${\pi \over {\sqrt 2 }}$$