Answer 1

The given function is f(x) = |x| - |x + 1|

The two functions, g and h, are defined as

Therefore, g is continuous at x = 0

From the above three observations, it can be concluded that g is continuous at all points.

Therefore, h is continuous at x = −1

From the above three observations, it can be concluded that h is continuous at all points of the real line.

g and h are continuous functions. Therefore, f = g − h is also a continuous function.

Therefore, f has no point of discontinuity.