The function `f(x) = [x] cos((2x-1)/2) pi` where [ ] denotes the greatest integer function, is discontinuousA. all xB. all integer pointsC. no xD. x which is not an integer

The function `f(x) = [x] cos((2x-1)/2) pi` where [ ] denotes the great

1.	The function `f(x) = [x] cos((2x-1)/2) pi` where [ ] denotes the greatest integer function, is discontinuousA. all xB. all integer pointsC. no xD. x which is not an integer
Answer» Correct Answer - C Here, `f(x) = [x] cos ((2x -1)/2) pi` f(x)=`:." "f(x)={{:(-cos((2x-1)/2)pi" ,"-1 le x lt 0),(0" , "0 le x lt 1),(cos((2x-1)/2) pi" , " 1 le x lt 2),(2 cos ((2x -1)/2) pi" , "2le x lt 3):}` which shows RHL = LHL at x = n `in ` Integer as if x = 1 `rArr underset( x to 1^(+)) lim cos((2x-1)/2) pi = 0 and underset ( x to 1^(-)) lim 0= 0 ` Also, f(1) = 0 `:.` Continous at x = 1. Similarly, when x = 2, ` underset( x to 2^(+)) lim f(x) = underset( x to 2^(-)) lim f(x) = 0 ` Thus, function is discontinuous at no x. Hence, option (c ) is the correct answer.