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Question

The number of points at which the function f(x)={[cosπx],0x1|x1|[x2],1<x2
is discontinuous, is
([.] denotes the greatest integral function )

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is D 4
For x=0,f(x)=1
For 0<x12,f(x)=0
For 12<x1,f(x)=1

For x(1,2),
[x2]=1 and |x1|=x1

For x=2, [x2]=0

f(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪1,x=00,0<x121,12<x1(x1),1<x<20,x=2

Clearly, f is discontinuous at four points i.e., {0,12,1,2} in the interval [0,2]

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