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Question

If f(x)={x24x+3x21,for x12,for x=1 , then

A
limx1+f(x)=2
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B
limx1f(x)=3
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C
f(x) is discontinuous at x = 1
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D
None of these
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Solution

The correct option is C f(x) is discontinuous at x = 1
f(x)={x24x+3x21} for x1
=2, for x = 1
f(1)=2,f(1+)=limx1+x24x+3x21=limx1+(x3)(x+1)=1
f(1)=limx1x24x+3x21=1f(1)f(1)
Hence the function is discontinuous at x = 1

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