Properties of Topological Groups

Question

I'm working though William Basener's Topology and Its Applications and I have come across a problem I can't solve. The book defines a topological group as a group equipped with a topology where for each element $a$, $L_{a} (x) = a + x$ and $R{a}(x) = x + a$ are both continuous. I need to prove that if the topology underlying the group is Hausdorff then $f(x, y) = x - y$ is continuous iff those all such functions $L$ and $R$ are continuous. Any ideas?