Find the points of discontinuity of the function

if they exist.

Solution.

The function exists for all

*x*, however it is defined by two different functions and, therefore, is not elementary.
We investigate "behavior" of the function near to the point

*x = *0
where its analytic expression changes.

Calculate one-sided limits at

*x = *0.

Thus, the function has a discontinuity of the first kind at

*x = *0.
The finite jump at this point is

The function is continuous for all other

*x*, because both the functions defined from the left and from the right of the point

*x = *0
are elementary functions without any discontinuities.