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  • Statement 1: Minimum number of points of discontinuity of the function <img alt="\mathrm{f(x)=(g(x))[2 x-1] \forall x \in(-3,-1)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf

Statement 1: Minimum number of points of discontinuity of the function \mathrm{f(x)=(g(x))[2 x-1] \forall x \in(-3,-1)},  where [.] denotes the greatest integer function and \mathrm{g(x)=a x^{3}+x^{2}+1}  is zero.

Statement 2: \mathrm{f(x)} can be continuous at a point of discontinuity, say \mathrm{x=c_{1}\: of \: [2 x-1]} if \mathrm{g\left(c_{1}\right)=0}.

Option: 1

Statement 1 is True, Statement 2 is True, Statement 2 is a correct explaination for Statement 1.


Option: 2

 Statement 1 is True, Statement 2 is True, Statement 2 is NOT a correct explanation for Statement 1.


Option: 3

Statement 1 is True, Statement 2 is False.


Option: 4

Statement 1 is False, Statement 2 is True


Answers (1)

best_answer

Clearly. \mathrm{[2 x-1]} is discontinuous at three points \mathrm{x=\frac{-5}{2}, \frac{-3}{2}} and \mathrm{-2}
\mathrm{f(x)} may be continuous if \mathrm{g(x)=a x^{3}+x^{2}+1=0} at \mathrm{x=\frac{-5}{2}, \frac{-3}{2}}

\mathrm{g(x)} can be zero at atleast one point

\mathrm{\therefore }  minimum number of points of discontinuity =2.

Posted by

Ritika Jonwal

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