Let \([\cdot]\) denote that greatest integer function. If the domain of the function \(f(x)=\sin ^{-1}\left(\frac{x+[x]}…

Let \([\cdot]\) denote that greatest integer function. If the domain of the function \(f(x)=\sin ^{-1}\left(\frac{x+[x]}{3}\right)\) is \([\alpha, \beta)\), then \(\alpha^2+\beta^2\) is equal to:

[JEE Main 2026, 6 Apr (Shift 1)]