What is an example of using aliasing to your advantage when recovering an input signal?
you can successfully recover (or reconstruct) the signal so long as $f_2&lt;F_s/2$


Nope. The sampling theorem says that you need 2 samples per Hz of bandwidth, so in this case you'd need 

$$Fs &gt; 2*(f_2-f_1)$$

For more info on how this works google "bandpass sampling" or just read https://en.wikipedia.org/wiki/Undersampling.

The basic idea is that sampling creates a periodic repetition of the original spectrum with a period of $F_s$. As long as none of the repeated spectra falls on the same frequencies as the original spectrum, you don't get aliasing.