The Total solution for NCERT class 6-12
Findall points of discontinuity of f, where f is definedby
The given function f is
It isevident that the given function f is defined at all the pointsof the real line.
Let c bea point on the real line. Then, three cases arise.
(i) c <2
(ii) c >2
(iii) c =2
Therefore, f iscontinuous at all points x, such that x < 2
Therefore, f iscontinuous at all points x, such that x > 2
Case(iii) c = 2
Theright hand limit of f at x = 2 is,
It isobserved that the left and right hand limit of f at x =2 do not coincide.
Therefore, f isnot continuous at x = 2
Hence, x =2 is the only point of discontinuity of f.