Domain of `g(x)={x:x in` domain of `g(x) and g(x)in` domain of `f(x)` and domain of `fog(x)` has atleast 3 elements)

Let f(x) = sqrt(2-x-x^(2)) and g(x) = cos x . Which of the following statement are true ? (I) Domain of f((f(x))^(2)) = Domain of f(g(x)) (II) Domain of f(g(x)) + g(f(x)) = Domain of f(g(x)) (III) Domain of f(g(x)) = Domain of f(g(x)) (IV) Domain of g((f(x))^(3)) = Domain of f(g(x))

If f(x) = sqrtx and g(x) = 2x -3 , then domain of (fog) (x) is

If f(x)=sqrt(3|x|-x-2) and g(x)=sin x then domain of (fog)(x) is

If domain of y=f(x) is xin[-3,2] , then the domain of f([x]) is

If domain of y=f(x) is xin[-3,2] , then the domain of f([x]) is

If f(x) = sqrt(2-x) and g(x) = sqrt(1-2x) , then the domain of fog (x) is

If f(x) = sqrt(2-x) and g(x) = sqrt(1-2x) , then the domain of fog (x) is

If f(x) and g(x) are polynomial functions of x, then domain of (f(x))/(g(x)) is

If f(x) and g(x) are polynomial functions of x, then domain of (f(x))/(g(x)) is

find the domain of g(x) 1/sqrt(|x|-x)