Number of elements in domain of `sqrt(fg)` if `f : {1,2,3} ->A, f(x) = x-1, g : {1,2,3} ->B,g(x) = x-2` is

Number of elements in the domain of the function is f(x)=sin^(-1)((x^(2)-2x)/(3))+sqrt([x]+[-x])

A is the domain of f(x) =1/sqrt(|x|-x) and B is the domain of g(x) = sqrt(1-|x|) then A cap B =

consider the functions f(x) = sqrt(x-2) , g(x) = ( x+1)/( x^2 -2x +1) (fg)(x)

If the domain of f(x)is[-1,3], then the domain g(x)=f(x^(2)-2x) is

consider the functions f(x) = sqrt(x-2) , g(x) = ( x+1)/( x^2 -2x +1) domain of g

consider the functions f(x) = sqrt(x-2) , g(x) = ( x+1)/( x^2 -2x +1) domain of f

If f and g are functions defined by : f(x) =sqrt(x - 1), g(x) = (1)/(x) , then describe the following : (i) f + g (ii) f - g (iii) fg (iv) (f)/(g) .

If f(x)=sqrt(|3^(x)-3^(1)|-2) and g(x)=tan pi x, then domain of fog(x) , is

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))