Easy functional equation (maybe)
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Find all $f : \mathbb{R} \rightarrow \mathbb{R}$ such that $\ f(f(x)) = f(x-1)+1 \ $
Last edited by tanmoy on Tue Mar 30, 2021 6:15 pm, edited 1 time in total.
Reason: The author didn't use Latex.
Reason: The author didn't use Latex.
Hmm..Hammer...Treat everything as nail
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Re: Easy functional equation (maybe)
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try inserting f-1(x) in the place where there's f(x) that should do it
Now you have to look at the problem from a different angle here
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try inserting f-1(x) in the place where there's f(x) that should do it
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Re: Easy functional equation (maybe)
did you mean f-1(x) as inverse function?
How would you prove it has inverse?? Or the fuction is Bijective?
Hmm..Hammer...Treat everything as nail
Re: Easy functional equation (maybe)
$f(x)=x$ This satisfies the equation. Right?
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Re: Easy functional equation (maybe)
satisfies but it is not only the solution it has infinite solutions
Hmm..Hammer...Treat everything as nail
Re: Easy functional equation (maybe)
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
- Mehrab4226
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Re: Easy functional equation (maybe)
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
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré
-Henri Poincaré