question_answer

The value of f(0) so that the function \[f\,\,(x)=\frac{{{\cos }^{-1}}(1-{{\{x\}}^{2}})\,\,{{\sin }^{-1}}\,\,(1-\{x\})}{\{x\}-{{\{x\}}^{3}}},\]\[x\ne 0\]({x} denotes fractional part of x) becomes continuous at x = 0 is

A)  \[\frac{\pi }{\sqrt{2}}\]                         

B)  \[\frac{\pi }{4}\]

C)  \[\frac{\pi }{2}\]                                   

D)  \[\frac{\pi }{8}\]

E)  None of these