# Find All the Points of Discontinuity Of F Defined by F(X) = |X| - |X + 1|. - Mathematics

Find all the points of discontinuity of defined by f(x) = |x| - |x + 1|.

#### Solution

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, g − is also a continuous function.

Therefore, has no point of discontinuity.

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#### APPEARS IN

NCERT Class 12 Maths
Chapter 5 Continuity and Differentiability
Q 34 | Page 161