Find the value of x for which `f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1) (2 sqrt(x - x^(2)))` is constant

If f(x) = 2 sin^(-1)sqrt(1-x) +sin^(-1)(2-sqrt(x(1-x)) where x in (0,(1)/2) , then f'(x) is

Find the domain of the following : f(x) = sqrt (1-2x)+3 sin^(-1) ((3x-1)/2) .

Find the domain of the function F(x) = tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1)

Find the value of x in [-pi,pi] for which f(x)=sqrt(log_(2)(4sin^(2)x-2sqrt(3)sin x-2sin x+sqrt(3)+1)) is defined.

Find (dy)/(dx), if y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))]

Range of f(x) =sin^-1(sqrt(x^2+x+1)) is

Range of f(x) =sin^-1(sqrt(x^2+x+1)) is