Consider the following statements: 1. f(x)=[x] , where [.] is the greatest integer function, is discontinuous at x=n , where n Z . 2. f(x)= x is discontinuous at x=n , where n Z . which of the above statements is/are correct?

Step-by-step solution

From statement-1 From the definition of greatest integer function f(x)=[x] is discontinuous at x=n for any value of n Z Statement 1 is correct From statement-2 f ( x )= x for x= = =- for x =2 f (2 )= 2 =- Hence the function f(x)= x is discontinuous at x = n where n Z . Option (C) is correct.