I've been set a question and I just want to verify I have understood it and would like a few pointers on solving it.

Given R=C[0,1]

-Firstly this is any function that is continuous on the domain [0,1] ?

I.e. f:[0,1] -> Reals

-The group of units is all continuous functions that are invertible on [0,1].

By my understanding: those that have no asymptotes (continuity), and no roots (invertibility) on [0,1].

Is there any way to classify these functions more rigourously?

Thanks