Find the domains of defination of the following functions:
(a) `f(x)=sqrt(x^(3)-x^(2))`,
(b `f(x)=sqrt(sin sqrtx)`
(c) `fx)=sqrt(-sin^(2) pix)`,
(d) `f(x)=(1)/sqrt(|x|-x|) and g(x)=1/sqrt(x-|x|)`
(e) `f(x)=arc sin (|x|x-3)`,
(f) `f(x)=arc cos ""1/(sin x)`

Answer

(a) `(1, +oo); (b) (2npi)^(2) le x le (2n+1)^(2) pi^(2) (n=0,1,2,.....)`
(c) `x=0, pm 1, +2,.....; (d) (-oo,0)` (e) `[-4,2] or [2,4]`
`(f) x=(2n+1) pi/2 (n=0, pm1, pm2,...)`