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  •  The number of points of discontinuity of <img alt="\mathrm{f(x)=[2 x]^{2}-(2 x)^{2}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%5B2%20x%5D%5E%7B2%7D-%282%20

 The number of points of discontinuity of \mathrm{f(x)=[2 x]^{2}-(2 x)^{2}} (where [ ] denotes the greatest integer function and \mathrm{\left \{ \right \}} is fractional part of \mathrm{x} )  in the interval \mathrm{(-2,2)},is

Option: 1

1


Option: 2

6


Option: 3

2


Option: 4

4


Answers (1)

best_answer

Given, \mathrm{f(x)=([2 x]+\{2 x\})([2 x]-\{2 x])=4 x-4 x\{2 x\}2 x \in(-4,4)}

Hence \mathrm{f(x)} is discontinuous when \mathrm{2 x=-3,-2,-1,1,2,3}. At \mathrm{x=0, f(x)} is continuous.
 

Posted by

Ajit Kumar Dubey

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