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Question

The number of points of discontinuity and non-differentiability of the function f(x) in its domain are respectively

A
2, 1
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B
2, 2
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C
1, 1
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D
1, 2
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Solution

The correct option is B 2, 2
f(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪x+2,2<x<11,1x<00x=010<x<111x<2

f(x)=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪x+2,2<x<11,1x<00,x=01,0<x<2

f(f(x))=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪f(x)+2,2<f(x)<11,1f(x)<00,f(x)=01,0<f(x)<2

f(f(x))=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪1,1x<00x=01,0<x<2x+2,2<x<1

f(f(x))=f(x)
Graph of f(x)

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