The number of discontinuous points of f(x) = 1/(x − [x]) is: A. All integers B. No point C. All real numbers D. Only at x = 0 Answer: A) All integers Explanation: x − [x] is fractional part, zero at integers. So 1/(x−[x]) is not defined at integers, thus discontinuous at all integers.

imo class 12 continuity and differentiability

The number of discontinuous points of f(x) = 1/(x − [x]) is:

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The number of discontinuous points of f(x) = 1/(x − [x]) is:

Answer: A) All integers

Explanation: x − [x] is fractional part, zero at integers. So 1/(x−[x]) is not defined at integers, thus discontinuous at all integers.