Question

Find the points of discontinuity of f, where

f (x) = sinx /x,if x< 0

f(x) = x+1 ,if x  ≥  0

Answer 1

It is evident that f is defined at all points of the real line. Let c be a real number.

Case I:

Therefore, f is continuous at all points x, such that x < 0 

Case II:

Therefore, f is continuous at all points x, such that x > 0 

Case III:

Therefore, f is continuous at x = 0
From the above observations, it can be concluded that f is continuous at all points of the real line. Thus, f has no point of discontinuity.