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Given f(x)={3-[cot^(-1)((2x^3-3)/(x^2))]...

Given `f(x)={3-[cot^(-1)((2x^3-3)/(x^2))]forx >0{x^2}cos(e^(1/x))forx<0` (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good? `f(0^-)=0` b. `f(0^+)=3` c. if `f(0)=0` , then `f(x)` is continuous at `x=0` d. irremovable discontinuity of `f` at `x=0`

A

`f(0^(-))=0`

B

`f(0)=3`

C

`f(0) rArr 0 rArr` continuity of f at `x=0`

D

irremovable discontinuity of f at x=0

Text Solution

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The correct Answer is:
A, C
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