The given function is defined at all pointsof the real line.
Let c bea point on the real line.
Case I:
Therefore, f iscontinuous at all points x, such that x < −1
Case II:
Theleft hand limit of f at x = −1 is,
Theright hand limit of f at x = −1 is,
Therefore, f iscontinuous at x = −1
Case III:
Therefore, f iscontinuous at all points of the interval (−1, 1).
Case IV:
Theleft hand limit of f at x = 1 is,
Theright hand limit of f at x = 1 is,
Therefore, f iscontinuous at x = 2
Case V:
Therefore, f iscontinuous at all points x, such that x > 1
Thus,from the above observations, it can be concluded that f iscontinuous at all points of the real line.