Groups and the Group Axioms · Medium problem

Let $S=\{f_a(x)=2x+a : a\in\mathbb Z\}$, a set of functions on $\mathbb Z$, with $*$ defined by composition, $f_a*f_b=f_a\circ f_b$. Computing $(f_3\circ f_5)(x)$ gives a function of the form $4x+c$ (not of the form $f_a(x)=2x+a$, showing $S$ is not closed under $*$). Find $c$.