It is evident that the given function f is defined at all the points of the real line. Let c be a point on the real line. Then, three cases arise.
(i) c < 2
(ii) c > 2
(iii) c = 2
Case (i) c < 2
Therefore, f is continuous at all points x, such that x < 2 Case (ii) c > 2
It is observed that the left and right hand limit of f at x = 2 do not coincide. Therefore, f is not continuous at x = 2 Hence, x = 2 is the only point of discontinuity of f.
