Please do mention the source (i think i have seen it in the shortlist)
FE Marathon!
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Hmm..Hammer...Treat everything as nail
Re: FE Marathon!
2004 IMO SLAsif Hossain wrote: ↑Sat Feb 27, 2021 8:59 amPlease do mention the source (i think i have seen it in the shortlist)
Re: FE Marathon!
$Problem 16$
Find all function such that $f:R \rightarrow R$ and
$f(xf(y)+y)+f(xy+x)=f(x+y)+2xy$
Find all function such that $f:R \rightarrow R$ and
$f(xf(y)+y)+f(xy+x)=f(x+y)+2xy$
Re: FE Marathon!
$\textbf{Problem 17}$
Find all functions $f: \mathbb R \to \mathbb R$ such that\[ f( xf(x) + f(y) ) = f(x)^2 + y \]for all $x,y\in \mathbb R$.
Find all functions $f: \mathbb R \to \mathbb R$ such that\[ f( xf(x) + f(y) ) = f(x)^2 + y \]for all $x,y\in \mathbb R$.
Last edited by ~Aurn0b~ on Sat Feb 27, 2021 8:09 pm, edited 1 time in total.
Re: FE Marathon!
$f^2(x)=f(f(x)) $ or $f^2(x)=(f(x))^2$
- Mehrab4226
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Re: FE Marathon!
THis one looks kinda okay, right?
The question changed so, this solution is no longer valid
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
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Re: FE Marathon!
Hmm..Hammer...Treat everything as nail