Question

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

A
integers n
B
integers n except n=0 and 1
C
integers n except n=0 and 1, since f(n)f(n)
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 =limx→n− [x]3−[x3]          =(n−1)3−(n3−1)=−3n(n−1) RHL =limx→n+ [x]3−[x3]=n3−n3=0 f(x) is continuous at n if f(n)=−3n(n−1)=0 therefore, f(x) is continuous at n=0 and 1 and discontinuous at Z−{0,1}

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