A group homomorphism proof with composition

A group homomorphism proof with composition

pSuppose I have groups $X$, $Y$, and $Z$, and I let $f: X \longrightarrow
Y$ and $g: Y \longrightarrow Z$ be group homomorphisms. Now, I want to
prove that $g \circ f : X \longrightarrow Z$ is a group homomorphism as
well. Here is my attempt:/p pLet $x, x' \in X$. Then,/p p$(g \circ f)(xx')
= g(f(xx'))$/p p$= g(f(x)f(x'))$/p p$= (g \circ f)(x)(g \circ f)(x')$/p
pThus, $g \circ f$ is a group homomorphism./p