Answer : f(x)=4[x-3]+2 discontinuous in all integers
f(x) is a floor function
Floor function gives the greatest integer < = given nnumber. Floor function always gives the greatest integer output.
For example , floor (2.25) = 2
2 is the greatest integer less than or equal to 2.25
f(x)=4[x-3]+2
When x= 1, then y = 4(-2) +2 = -6
When x= 1.5, then y= 4(-2) +2 = -6 [floor (1.5-3) = floor (-1.5) = -2]
When x= 2, then y= 4(-1) +2 = -2
When x= 2.5, then y= 4(-1) +2 = -2 [floor (2.5-3) = floor (-0.5) = -1]
When x= 3, then y= 4(0) +2 = 2
When x= 3.5, then y= 4(0) +2 = 2 [floor (3.5-3) = floor (0) = 0 ]
We can see that the y value changes for every integer like x=1, 2, 3 and so on
So answer is all integers.
