MHT CET · Maths · Continuity and Differentiability
Let \(\mathrm{f}(x)=x\left[\frac{x}{2}\right]\), for \(-10 \lt x \lt 10\), where \([\mathrm{t}]\) denotes the greatest integer function. Then the number of points of discontinuity of \(f\) is equal to
- A 10
- B 9
- C 6
- D 8
Answer & Solution
Correct Answer
(D) 8
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
& -10 \lt x \lt 10 \\
& \Rightarrow-5 \lt \frac{x}{2} \lt 5 \\
& \Rightarrow \frac{x}{2}=0, \pm 1, \pm 2, \pm 3, \pm 4
\end{aligned}\)
But \(\mathrm{f}(x)\) is continuous at \(x=0\).
\(\therefore \quad\) There are 8 points of discontinuity i.e. \(-4,-3\), \(-2,-1,1,2,3,4\).
& -10 \lt x \lt 10 \\
& \Rightarrow-5 \lt \frac{x}{2} \lt 5 \\
& \Rightarrow \frac{x}{2}=0, \pm 1, \pm 2, \pm 3, \pm 4
\end{aligned}\)
But \(\mathrm{f}(x)\) is continuous at \(x=0\).
\(\therefore \quad\) There are 8 points of discontinuity i.e. \(-4,-3\), \(-2,-1,1,2,3,4\).
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