Let $f (x) = [3 x^{3} - 10], []$ denote the greatest integer function then number of points in $(1, 2)$ where the function is discontinuous is

7

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20

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0

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21

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Solution

The correct option is B $20$
Let $g (x) = 3 x^{3} - 10$ , which is an increasing function $\forall x \in R$ so also increasing function in $(1, 2)$ and $g (1) = - 7, g (2) = 14$ , every greatest integer function is discontinuous at all integral points and number of integers between $- 7$ and $14$ are $20$ , shown by the number line

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Let f(x)=[3x3−10],[] denote the greatest integer function then number of points in (1,2) where the function is discontinuous is

The correct option is B 20Let g(x)=3x3−10, which is an increasing function ∀x∈R so also increasing function in (1,2) and g(1)=−7,g(2)=14, every greatest integer function is discontinuous at all integral points and number of integers between −7 and 14 are 20, shown by the number line

Let $f (x) = [3 x^{3} - 10], []$ denote the greatest integer function then number of points in $(1, 2)$ where the function is discontinuous is