Question about the properties of iterated functions

[Shanghai46]

Yes that is true if the function is continu and monotone on that interval.

Notice a violation would imply there is another fixpoint in the interval but that violates the conditions.
So it must be true then if  the function is continu and monotone on that interval.

So basically if f(x) is continu and f'(x) is never 0 or infinite on that closed interval.

Notice monotone implies the function and its inverse have unique inverses on that interval.
The inverse of a continu and monotone function is continu and monotone too afterall.



regards

tommy1729

Thank you really much! I was almost sure of that but I needed confirmation. I almost finished putting all restrictions to my fractional iterated function formula, then I'll demonstrate it. I just have one last problem to solve.