Question -
Answer -
The given function f is 
Thegiven function f is defined at all the points of the realline.
Let c bea point on the real line.
Case I:
Therefore, f iscontinuous at all points x, such that x < 1
Case II:
If c =1, then the left hand limit of f at x = 1 is,
Theright hand limit of f at x = 1 is,
It isobserved that the left and right hand limit of f at x =1 do not coincide.
Therefore, f isnot continuous at x = 1
Case III:
Therefore, f iscontinuous at all points x, such that x > 1
Thus,from the above observation, it can be concluded that x = 1 isthe only point of discontinuity of f.