Is the following homomorphism continuous?

Question

Let $G$ be a closed, torsion-free and divisible subgroup of locally compact abelian group $X$ such that $nX=G$ for some $n$. For $x\in X$, there exist $g\in G$ such that $nx=ng$. So we can define a homomorphism $f:X\to G$, $f(x)=g$. Now, my question: Is $f$ continuous?