Easy functional equation (maybe)
Posted: Thu Feb 18, 2021 12:33 pm
Find all $f : \mathbb{R} \rightarrow \mathbb{R}$ such that $\ f(f(x)) = f(x-1)+1 \ $
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Easy functional equation (maybe)
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Re: Easy functional equation (maybe)
Posted: Fri Feb 19, 2021 1:53 pm
Still no answer
Re: Easy functional equation (maybe)
Posted: Fri Feb 19, 2021 3:24 pm
Now you have to look at the problem from a different angle here
[img]
try inserting f-1(x) in the place where there's f(x) that should do it
Re: Easy functional equation (maybe)
Posted: Sat Feb 20, 2021 9:26 am
did you mean f-1(x) as inverse function?
How would you prove it has inverse?? Or the fuction is Bijective?
Re: Easy functional equation (maybe)
Posted: Tue Mar 30, 2021 5:22 pm
$f(x)=x$ This satisfies the equation. Right?
Re: Easy functional equation (maybe)
Posted: Tue Mar 30, 2021 9:10 pm
Re: Easy functional equation (maybe)
Posted: Sat Apr 03, 2021 1:57 pm
How to solve this? I can not solve functional equations. Can amyone help by giving solution to this? Besides, can anyone suggest me any book to practice functional equation?Asif Hossain wrote: ↑Tue Mar 30, 2021 9:10 pmsatisfies but it is not only the solution it has infinite solutions
Re: Easy functional equation (maybe)
Posted: Sun Apr 04, 2021 9:25 am
Read the note here, it may be helpful.Mahee2166 wrote: ↑Sat Apr 03, 2021 1:57 pmHow to solve this? I can not solve functional equations. Can amyone help by giving solution to this? Besides, can anyone suggest me any book to practice functional equation?Asif Hossain wrote: ↑Tue Mar 30, 2021 9:10 pmsatisfies but it is not only the solution it has infinite solutions
https://web.evanchen.cc/handouts/FuncEq ... -Intro.pdf