SOLUTION: The function f(x)= sqrt(sin(x)(sin(x) -2)+1) is continuous at x = pi/2. ( true or {{{highlight(cross(fals))}}} <U>false</U>) ?

Consider function  


    sin(x)*(sin(x)-2)+1) = sin^2(x) - 2sin(x) + sin(x) = sin^2(x) - sin(x) = sin(x)*(sin(x) -1).


In vicinity of  x=   this function is negative (except of its value at x= , where it is zero).


Therefore, in vicinity of  x =   the given expression, which is the square root of sin(x)*(sin(x)-2)+1),
is not defined, at all, as a real function, so the question  "is it continuous or not"

even can not be posed: this function does not exist in real domain.