MHT CET · Maths · Continuity and Differentiability
The function \(\mathrm{f}(x)=[x] \cdot \cos \left(\frac{2 x-1}{2}\right) \pi\), where \([\cdot]\) denotes the greatest integer function, is discontinuous at
- A (A) all irrational numbers \(x\).
- B no \(x\).
- C all integer points.
- D every rational \(x\) which is not an integer.
Answer & Solution
Correct Answer
(C) all integer points.
Step-by-step Solution
Detailed explanation
Greatest integer function is discontinuous on integer values.
\(\therefore \quad \mathrm{f}(x)\) is discontinuous at all integer points.
\(\therefore \quad \mathrm{f}(x)\) is discontinuous at all integer points.
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