# Thread: Inverse functions

1. ## Inverse functions

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

2. Originally Posted by mrmango
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
Well, $\mathcal{C}[E],\text{ }E\subseteq \mathbb{R}$ is the set of all bounded functions $f:E\mapsto\mathbb{R}$ continuiously. In your case you just lucked out that continuity implies boundedness.

-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
I'm not sure what you mean here? You can turn $\mathcal{C}[0,1]$ into a ring?

3. Thanks for your reply,

Im pretty sure it is a ring, but correct me if i'm wrong

Thanks again

4. Originally Posted by mrmango
Thanks for your reply,

Im pretty sure it is a ring, but correct me if i'm wrong

Thanks again
It is a ring.