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Question

Let g(x)=2(x+1),<x11x2,1<x<1|x+1|,1x< then

A
g(x) is discontinuous at exactly three points
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B
g(x) is continuous in (,1]
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C
g(x) is continuous in [1,)
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D
g(x) has finite type of discontinuity at x=1, but continuous at x=1
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Solution

The correct option is D g(x) has finite type of discontinuity at x=1, but continuous at x=1
g(x)=2(x+1),<x11x2,1<x<1thenx+1,1
At x=1
L.H.L(Left Hand Limit)
limx 1f(x)=2(1+1)=0
R.H.L(Right Hand Limit)
limx 1+f(x)=1(1)2=0
L.H.L=R.H.L(at X=0)
At x=1
L.H.L=limx 1+f(x)=112=0
R.H.L=limx 1+f(x)=1+1=2
L.H.L R.H.L(at x=2)
But it is finite.

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