Easy functional equation (maybe)

For students of class 9-10 (age 14-16)
Asif Hossain
Posts:194
Joined:Sat Jan 02, 2021 9:28 pm
Easy functional equation (maybe)

Unread post by Asif Hossain » Thu Feb 18, 2021 12:33 pm

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.
Hmm..Hammer...Treat everything as nail

Asif Hossain
Posts:194
Joined:Sat Jan 02, 2021 9:28 pm

Re: Easy functional equation (maybe)

Unread post by Asif Hossain » Fri Feb 19, 2021 1:53 pm

Still no answer :roll:
Hmm..Hammer...Treat everything as nail

User avatar
Safwan
Posts:18
Joined:Tue Jan 15, 2019 8:50 pm
Location:BAU,Mymensingh,Bangladesh

Re: Easy functional equation (maybe)

Unread post by Safwan » Fri Feb 19, 2021 3:24 pm

Image[/img][/img][/img]
Asif Hossain wrote:
Thu Feb 18, 2021 12:33 pm
find all f:R->R such that f(f(x))= f(x-1)+1
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 :)

Asif Hossain
Posts:194
Joined:Sat Jan 02, 2021 9:28 pm

Re: Easy functional equation (maybe)

Unread post by Asif Hossain » Sat Feb 20, 2021 9:26 am

Safwan wrote:
Fri Feb 19, 2021 3:24 pm
Image[/img][/img][/img]
Asif Hossain wrote:
Thu Feb 18, 2021 12:33 pm
find all f:R->R such that f(f(x))= f(x-1)+1
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 :)
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

Mahee2166
Posts:2
Joined:Tue Mar 30, 2021 5:17 pm

Re: Easy functional equation (maybe)

Unread post by Mahee2166 » Tue Mar 30, 2021 5:22 pm

$f(x)=x$ This satisfies the equation. Right?

Asif Hossain
Posts:194
Joined:Sat Jan 02, 2021 9:28 pm

Re: Easy functional equation (maybe)

Unread post by Asif Hossain » Tue Mar 30, 2021 9:10 pm

Mahee2166 wrote:
Tue Mar 30, 2021 5:22 pm
$f(x)=x$ This satisfies the equation. Right?
satisfies but it is not only the solution it has infinite solutions :D
Hmm..Hammer...Treat everything as nail

Mahee2166
Posts:2
Joined:Tue Mar 30, 2021 5:17 pm

Re: Easy functional equation (maybe)

Unread post by Mahee2166 » Sat Apr 03, 2021 1:57 pm

Asif Hossain wrote:
Tue Mar 30, 2021 9:10 pm
Mahee2166 wrote:
Tue Mar 30, 2021 5:22 pm
$f(x)=x$ This satisfies the equation. Right?
satisfies but it is not only the solution it has infinite solutions :D
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?

User avatar
Mehrab4226
Posts:230
Joined:Sat Jan 11, 2020 1:38 pm
Location:Dhaka, Bangladesh

Re: Easy functional equation (maybe)

Unread post by Mehrab4226 » Sun Apr 04, 2021 9:25 am

Mahee2166 wrote:
Sat Apr 03, 2021 1:57 pm
Asif Hossain wrote:
Tue Mar 30, 2021 9:10 pm
Mahee2166 wrote:
Tue Mar 30, 2021 5:22 pm
$f(x)=x$ This satisfies the equation. Right?
satisfies but it is not only the solution it has infinite solutions :D
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?
Read the note here, it may be helpful.
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

Post Reply