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

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