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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?%5Cmath

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 discontinuously, say \mathrm{x=c_1 \text { of }[2 r-1] \text { if } g\left(c_1\right)=0 \text {. }}

Option: 1

Statement I is true, statement 2 is true, statement 2 is a correct explanation for statement I.


Option: 2

Statement I is true, statement 2 is true, statement 2 is a NOT a correct explanation for statement I.


Option: 3

Statement I is true, statement 2 is false.


Option: 4

Statement I is true, statement 2 is true, 


Answers (1)

best_answer

Clearly, [2x-1] is discontinuous at three points  \mathrm{x=\frac{-5}{2}, \frac{-3}{2}} and -2

f(x) may be continuous if \mathrm{g(x)=a x^3+x^2+1=0 \text { at } x=\frac{-5}{2}, \frac{-3}{2}}

 or -2

g(x) can be zero ztleast one point

\therefore minimum number of points of discontinuity=2

Posted by

Sanket Gandhi

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