Logic function of cmos circuit with feedback
Simply determine when f1 is pulled to ground:

this is when not(a) and not(b) are both high.

So:

f1 = 1 when a = 0 AND b = 0


Now when is f2 pulled to ground:

f2 is zero when a = 1 OR b = 1


So truth table:

a  b   f1  f2
0  0   1   0
0  1   0   1
1  0   0   1
1  1   0   1


So:

f1 = not( a OR b)


and

f2 = (a or b)


You can effectively ignore the two PMOS at the top, this circuit only allows
f1 = f2 = 1  (all NMOS would be off but this cannot happen in this circuit)
or
f1 = not(f2)
so basically an inversion.