Homomorphism and group problem

For each $a \ne 0$ and $b$ in $GF(7) = \bold{Z}_7$ define a function $\mathit{F}_{a,b}:\bold{Z}_7\rightarrow \bold{Z}_7$ by

$\mathit{F}_{a,b}(x) = ax + b$

The set of all such function $\mathit{F}_{a,b}$ forms a group $g$ with the group multiplication given by the compostion of the functions.(Not need to verify $G$ is a group)

a. Determine $|G|$ and find $\mathit{F}_{a,b}\circ \mathit{F}_{c,d} = \mathit{F}_{a,b}(\mathit{F}_{c,d}(x))$ . Hence show that $G$ is non-abelian.

b. Show that $\mathit{f}:G\rightarrow(\bold{Z}_7\setminus {0},\cdot )$ ,given by $\mathit{f}(\mathit{F}_{a,b})=a$ , is a homomorphism.

I'm OK with the $|G|$ part but I forget how to show $\mathit{F}_{a,b}\circ \mathit{F}_{c,d} = \mathit{F}_{a,b}(\mathit{F}_{c,d}(x))$ .
Also for part b, I don't really get it.

Thank you for help