Hello,

I've got to solve a following problem.

f is a function like this . And two sets . I've got to figure out how are the following two sets related:

and

I got to here:

Can I assume through this that ? If so then how to correctly justify it?

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- Dec 3rd 2012, 02:16 PMMachinePL1993Proof regarding inverse functions
Hello,

I've got to solve a following problem.

f is a function like this . And two sets . I've got to figure out how are the following two sets related:

and

I got to here:

Can I assume through this that ? If so then how to correctly justify it? - Dec 3rd 2012, 02:26 PMPlatoRe: Proof regarding inverse functions
- Dec 3rd 2012, 02:54 PMMachinePL1993Re: Proof regarding inverse functions
Then

So is the following proof correct?

So let's assume that set is defined like this , this means that and .

So let's take any such that , then

Since , this means that

So I have proven that , in other words

But is not a subset of which can be proven by a counterexample like the one above.

Is this right? - Dec 3rd 2012, 03:04 PMPlatoRe: Proof regarding inverse functions