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Question

f(x)=[x]3[x3], (where [.] is greatest integer function) is discontinuous at all 


Your Answer
A
integers n
Correct Answer
B
integers n except n=0 and 1
Correct Answer
C
integers n except n=0 and 1, since f(n)f(n)
Your Answer
D
integers n except n=0 and 1, since f(n+)f(n)

Solution

The correct options are
B integers n except n=0 and 1
C integers n except n=0 and 1, since f(n)f(n)
Let n z
LHL =limxn [x]3[x3]          =(n1)3(n31)=3n(n1)
RHL =limxn+ [x]3[x3]=n3n3=0
f(x) is continuous at n
if f(n)=3n(n1)=0
therefore, f(x) is continuous at
n=0 and 1 and discontinuous at Z{0,1}

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