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Statement 1: Minimum number of points of...

Statement 1: Minimum number of points of discontinuity of the function `f(x)=(g(x)[2x-1]AAx in (-3,-1)` , where [.] denotes the greatest integer function and `g(x)=a x^3=x^2+1` is zero. Statement 2: `f(x)` can be continuous at a point of discontinuity, say `x=c_1of[2x-1]ifg(c_1)=0.` Statement 1 is True, Statement 2 is True, Statement 2 isa correct explanation for Statement 1. Statement 1 is True, Statement 2 is True, Statement 2 is NOT a correct explanation for statement 1. Statement 1 is True, Statement 2 is False Statement 1 is False, Statement 2 is True.

A

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

B

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

C

Statement 1 is True, Statement 2 is False.

D

Statement 1 is False, Statement 2 is True.

Text Solution

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The correct Answer is:
D
Clearly, `[2x-1]` is dicontinuous at three points `x=(-5)/(2),(-3)/(2)` and `-2`
f(x) may be continuous if `g(x)=ax^(3)+x^(2)+1=0` at `x=(-5)/(2),(-3)/(2) or -2`
g(x) can be zero at atleast one point
`therefore" "` minimum number of points of discontinuity = 2.
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Statement 1: Minimum number of points of discontinuty of the function f(x)=(g(x)[2x-1]AA x in(-3,-1) where [.] denotes the greatest integer function and g(x)=ax^(3)+x^(2)+1 is zero.Statement 2:f(x) can be continuous at a point of discontinuity,say x=c_(1) of [2x-1] if g(c_(1))=0.

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