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Question

Let f(x)=x|xx2|,x[1,1]. Then the number of points at which f(x) is discontinuous is

A
1
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B
2
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C
0
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D
None of these
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Solution

The correct option is C 0
Given f(x)=x|xx2|.................[xϵ[1,1]]
Case1: xx20

x(1x)0
Hence xϵ[0,1]

Case2:xx2<0

x(1x)<0
Hence xϵ[1,0)

So,

x2x3......for 0x1
f(x)={
x3x2......for1x<0

Since,

limx0=limx0+.

So, function is continuous at x=0 So function is continuous in all points..


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