• Find the domain of function f(x) = ( sin^-1(3x-4x³) )^½

First> the while fn is in root means sin-1(3x-4x³) needs to be greater than 0 means 3x-4x³ is b/w 0 to 1 . means 0≤3x-4x³≤1 , x≤-√3/2, 0≤x≤√3/2 And x≥-1. Hence x belongs to (-1,-√3/2)+(0,√3/2). Please do approve my answer if correct