The number of points, where f(x)=[ x+ x] (where [.] denotes the greatest integer function) and x (0,2 ) is not continuous, is

Step-by-step solution

Given, aligned f(x) & =[ x+ x] & = [ 2 ( 1 2 x+ 1 2 x ) ] & = [ 2 (x+ 4 ) ] aligned We know that, greatest integer function is discontinuous on integer values. Function 2 (x+ 4 ) will gives integer values at x=90^ , 135^ , 180^ , 270^ , 315^ , Hence, there are five points in the given interval, in which f(x) is not continuous.