Let \( f(x)=\frac{\sin ^{-1}(1-\{x\}) \cos ^{-1}(1-\{x\})}{\sqrt{2\{x\}}(1-\{x\})} \). Then the value of \( \left(\frac{\lim _{x \rightarrow 0^{-}} f(x)}{\lim _{x \rightarrow 0^{+}} f(x)}\right)^{2} \) is equal to : (Here \( \{\cdot\} \) denotes fractional part function)
\( \frac{1}{2} \)
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