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Let f(x) = [x] and g(x) = {{:(0",",x in ...

Let `f(x) = [x] and g(x) = {{:(0",",x in Z),(x^(2)",",x in R - Z):}`, then (where `[*]` denotes greatest integer function)

A

`lim_(xto1)(g(x)` exists but `g(x)` is not continuous at `x=1`

B

`lim_(xto1)f(x)` does not exist and `f(x)` is not continuous at `x=1`

C

`g(x)` is continuous at `x=0`

D

`g(x)` is discontinuous at `x=0`

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