(8)

To determine the points of discontinuity of the function , where denotes the greatest integer function, we need to identify possible values of where discontinuities might occur within the interval .

Discontinuity Analysis
For the term :
The probable values of that could cause discontinuities are the roots or specific values where the integer part changes between consecutive integers. The transitions happen when:

For the term :
The values of where changes are straightforward. They occur at:

Discontinuity Check
By evaluating at all these potential points, we find the function is indeed discontinuous at:

Thus, the function has 8 discontinuities on the interval .

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