Find all functions f from the set of real numbers into the set of real
numbers which satisfy for all real x, y the identity
$f (x f (x+y)) = f (y f (x))+x^2$.
I'm trying to solve it for 5 hours but still couldn't solve ( ). I've prove its surjectivity but couldn't prove that it's injective.
IMO SL-7(2009)
- Sazid Akhter Turzo
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Re: IMO SL-7(2009)
I think the first red part means multiplying $x,f(x+y)$ and the second one means $x^2$Sazid Akhter Turzo wrote:Find all functions f from the set of real numbers into the set of real
numbers which satisfy for all real x, y the identity
f (x f (x+y)) = f (y f (x))+x2.
I'm trying to solve it for 5 hours but still couldn't solve ( ). I've prove its surjectivity but couldn't prove that it's injective.
[using latex would be good ]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: IMO SL-7(2009)
Edited and latexed.
@Sazid: Why don't you use latex?
http://www.matholympiad.org.bd/forum/vi ... p?f=25&t=2
@Sazid: Why don't you use latex?
http://www.matholympiad.org.bd/forum/vi ... p?f=25&t=2
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Nur Muhammad Shafiullah | Mahi
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Nur Muhammad Shafiullah | Mahi
- zadid xcalibured
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Re: IMO SL-7(2009)
plugging x=0 we get f(o)=f(yf(o)).this implies the functional equation is constant.but how?this is an sl prblm
Re: IMO SL-7(2009)
What if $f(0)=0$?Then all we get is $f(0)=0$.zadid xcalibured wrote:plugging x=0 we get f(o)=f(yf(o)).this implies the functional equation is constant.but how?this is an sl prblm
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Nur Muhammad Shafiullah | Mahi
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Re: IMO SL-7(2009)
oh sorry this only implies f(o)=o