The solution set of sgn x-3 =-1is ? A){x:x<3} B){x:x>3} C){x:x<-3} D){x:x>-3} ?

To solve the equation sgn x - 3 = -1, we can first add 3 to both sides of the equation:

sgn x - 3 + 3 = -1 + 3

This simplifies to:

sgn x = 2

The signum function (sgn x) returns -1 if x is negative, 0 if x is zero, and 1 if x is positive. Since we have sgn x = 2, which is not one of the possible outputs of the signum function, there is no solution to this equation.

Therefore, the correct answer is none of the above.