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Question

The function f(x)=[x]2[x2], where [y] is the greatest integer less than or equal to y, is discontinuous at

A
all integers
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B
all integers except 1
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C
all integers except 0
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D
all integers except 1
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Solution

The correct option is D all integers except 1
Given, f(x)=[x]2[x2]
Let x=n where nZ
limxn+f(x)=n2n2=0
limxnf(x)=(n1)2(n21)=2n+2f(n)=0

For the function to be continuous at x=n,
2n+2=0n=1
Hence, function is discontinuous at all integers except x=1.

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