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Let \mathrm{f(x)=\left[2 x^3-6\right]}, where [x] is the greatest integer less than or equal to x. Then the number of points in (1,2) where f is discontinuous is

Option: 1

5


Option: 2

7


Option: 3

13


Option: 4

12


Answers (1)

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For \mathrm{ x \in(1,2), 2<2 x^3<16 \Rightarrow-4<2 x^3- 6<10,2 x^3-6=-3,-2,-1,0,1,2, \ldots 9}. So there are 13 points at which the function f is discontinuous.

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