Timeline for Functional equation $f(f(f(x)f(y)))=f(x)f(y^2)$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 23, 2016 at 7:18 | review | Suggested edits | |||
| Jul 23, 2016 at 7:30 | |||||
| Jul 23, 2016 at 7:17 | vote | accept | wythagoras | ||
| Jul 22, 2016 at 22:03 | comment | added | elias | most appropriate username for this solution | |
| Jul 22, 2016 at 21:41 | comment | added | f'' | If $f$ must be continuous over $\mathbb{R}^+$, then yes, because $\lim_{x\rightarrow1}f(x)$ would not exist if it was not constant. | |
| Jul 22, 2016 at 21:36 | comment | added | Deusovi♦ | @QuestionAsker: Consider the function defined as "$1$ if $x=2^n$ for $n\in\mathbb N$ and $0$ otherwise". | |
| Jul 22, 2016 at 21:33 | comment | added | Shuri2060 | Thanks. Out of interest, is the solution to $f(x) = f(x^2)$ a constant in general (out of context of the question)? | |
| Jul 22, 2016 at 21:29 | comment | added | f'' | With $f(z)^2=f(f(f(z)))$, substitute $z=f(x)$. | |
| Jul 22, 2016 at 21:21 | comment | added | Shuri2060 | That's doing my brain in... how do you get $f(f(f(f(x)))) = f(f(x))^2$? I just about get every other part though - nice solution! | |
| Jul 22, 2016 at 21:04 | history | answered | f'' | CC BY-SA 3.0 |