Let α ∈ R be such that the function f(x)= {(cos^-1(1-{x}^2) sin^-1(1-{x}))/({x}-{x}^3), x ≠ 0; α, x=0} is continuous at x=0, where {x}=x-[x],[x] is…

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