Symmetrically continuous function

In mathematics, a function f : R → R is symmetrically continuous at a point x

The usual definition of continuity implies symmetric continuity, but the converse is not true. For example, the function x − 2 is symmetrically continuous at x = 0 , but not continuous.

Also, symmetric differentiability implies symmetric continuity, but the converse is not true just like usual continuity does not imply differentiability.