Find the domain of `f(x)=sqrt(cos^(-1)x-sin^(-1)x)`

Explanation

We must have `cos^(-1)x ge sin^(-1)x`
or `(pi)/(2)- sin^(-1)x ge sin^(-1)x`
or ` (pi)/(2) ge 2 sin^(-1)x`
or ` sin^(-1)x le (pi)/(4), " but " -(pi)/(2) le sin^(-1)x`
or `-(pi)/(2) le sin^(-1)x le (pi)/(4)`
or ` sin(-(pi)/(2)) le x le "sin"(pi)/(4)`
` " " ( :' sinx " is increasing function in " [-(pi)/(2),(pi)/(2)])`
or `x in [-1,(1)/(sqrt(2))]`