The given function is defined at all points of the real line. Let c be a point on the real line.
Case I:
Therefore, f is continuous at all points x, such that x < 0
Case II:
Therefore, f is continuous at x = 0
Case III:
Therefore, f is continuous at all points of the interval (0, 1).
Case IV:
It is observed that the left and right hand limits of f at x = 1 do not coincide.
Therefore, f is not continuous at x = 1
Case V:
Therefore, f is continuous at all points x, such that x > 1
Hence, f is not continuous only at x = 1
