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

Given `f(x)={{:(3-[cot^(-1)((2x^3-3)/(x^2))], x >0) ,({x^2}cos(e^(1/x)) , x<0):}` (where {} and [] denotes the fractional part and the integral part functions respectively). Then which of the following statements do/does not hold good?

A

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

B

`f(0^(+)) = 0`

C

`f(0) = 0 rArr` Continuous at x = 0

D

Irremovable discontinuity at x = 0

Text Solution

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The correct Answer is:

A, B, C

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