Find an isomorphism

Question

Let $G$ be the group of all real valued functions on the real line, under addition of functions. Let $H$ be the subset of $G$ consisting of all $f$ such that $f(0)=0$. Show that $G/H\cong (\mathbb{R},+)$.

I understand that I should use the First Isomorphism Theory. I am trying to find a surjective homomorphism but I got stuck there. Can someone help please?

Thanks

Answer 1

The evaluation $$G\longrightarrow\Bbb R$$ $$f\longmapsto f(0)$$ is an homomorphism with kernel...