Question -
Answer -
The given function f is
It isevident that f is defined at all points of the real line.
Let c bea real number.
Case I:
Therefore, f iscontinuous at all points x, such that x < 0
Case II:
Therefore, f iscontinuous at all points x, such that x > 0
Case III:
Theleft hand limit of f at x = 0 is,
Theright hand limit of f at x = 0 is,
Therefore, f iscontinuous at x = 0
Fromthe above observations, it can be concluded that f iscontinuous at all points of the real line.
Thus, f hasno point of discontinuity.