If f(x)=|x|−3,          x<1|x−2|+a,       x≥1  and g(x)=2−|x|         ,    x<2sgn(x)−b,              x≥2  and h(x)=f(x)+g(x) is continuous at exactly one point then which of the following value of a and b are not possible

f(x) is continuous for all x  if it is continuous atx=1 for which |1|−3=|1−2|+a  or a=−3 g(x) is continuous for all x  if its is continuous at x=2  for  which 2−|2|=sgn(2)−b=1−b  or b=1. Thus, f(x)+g(x) is continuous for all x  if a=−3,  b=1 Hence, f(x) is discontinuous at exactly one point for option (A).For option (B) f(x)  is discontinuous at one point and for option (C) f(x) is discontinuous at two points.