How to determine sampling frequency for an x(t) signal avoiding aliasing? The antitransform of the function is given:

$ \hat{x}(f) = \frac{123 + i246\pi f}{246 - 24600 \pi^2 f^2 + i4920\pi f} $

I'm asked to determine which frequency can I sample using the function x(t) avoiding aliasing? (or which range of values)

Update the problem actually suggest five answers:
100, 10, 1, 0.4 or none of these. Turns out the answer is none of these.
The function you show has a frequency range of $-\infty$ to $\infty$ so it isn’t strictly band limited. To completely avoid aliasing, it needs infinite sampling. 

Of course, you can use tables or Fourier identities to obtain the exact inverse.

Usually some acceptable criteria is specified for tolerable aliasing when specifying a sample rate.