honorable mathematicians,

I was asked to verify that the set $\displaystyle H = \{ f : f: \mathbb{R} \mapsto \mathbb{R} \mbox{ and } f(x) \ne 0 \mbox{ for all } x \in \mathbb{R} \}$ is a group with respect to multiplication. i did that, no problem. but then the question asks, "How does this group differ from the group of invertible (real) mappings?"

i have no idea what this question wants from me...

Thanks