I have 2 definitions for residually finite groups.

Definition 1: $\displaystyle G$ is said to be residually finite if for each nontrivial element, $\displaystyle x$ in $\displaystyle G$, there exists a finite index normal subgroup $\displaystyle N_x$ in G such that $\displaystyle x \notin N_x$.

Definition 2: $\displaystyle G$ is said to be residually finite if for each nontrivial element, $\displaystyle x \in G$, there exists a homomorphism $\displaystyle f$ from $\displaystyle G$ to a finite group, such thatf(x)is not the identity.

I have a problem in proving finite extension of residually finite groups are residually finite.

I have $\displaystyle 1 \longrightarrow K \longrightarrow G \longrightarrow Q \longrightarrow 1$, with $\displaystyle K$ is residually finite and $\displaystyle Q$ is finite.

Can anyone show me where to start or some hints?