Stuck on how to answer this. The most I've done is split it up using the relation, $f(bab) = f(a^{-1}) \Rightarrow f(b) + f(a) +f(b) = -f(a) \Rightarrow f(a) = -f(a)$, for the first one and $f(bab) = f(a^{-1}) \Rightarrow f(b) + f(a) +f(b) = -f(a) \Rightarrow 6 + f(a) = -f(a)$, for the second.
For the first one, my answer is that there are 2 group homomorphisms because $0 = 0$ and $3=-3$ are the only two that satisfy, i.e $im(f) = \{0,3\}$.
But for the second, I'm not getting the right answer. Would appreciate help.
Fir the second one, we want $f(b)=3$, but what does that tell us about $f(b^2)$? Do you see a problem there?