Let \(\alpha \in R\) be such that the function \(f\left(x\right)=\left{\begin{matrix}\frac{{\text{cos}}^{−1}\left(1−{{x}…

Let \(\alpha \in R\) be such that the function
\(f\left(x\right)=\left{\begin{matrix}\frac{{\text{cos}}^{−1}\left(1−{{x}}^{2}\right){\text{sin}}^{−1}\left(1−\left{x\right}\right)}{\left{x\right}−{{x}}^{3}},x\neq 0 \\ \text{      }\alpha ,\text{                }x=0\end{matrix}\right.\)

is continuous at \(x=0\), where \(\{x\}=x-[x],[x]\) is the greatest integer less than or equal to \(x\).

[JEE Main 2021, 16 Mar (Shift 2)]