2006 MOSP Homework Algebra 1.2

by djmathman, Feb 13, 2013, 12:39 AM

Problem wrote:
Find all functions $f:\mathbb{R}\to\mathbb{R}$ satisfying

\[f(x+f(y))=x+f(f(y))\]
for all real numbers $x$ and $y$, with the additional constraint that $f(2004)=2005$.

EDIT: Now this is right
This post has been edited 2 times. Last edited by djmathman, Feb 13, 2013, 3:09 AM

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5 Comments

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dude $f$ isn't surjective

by dinoboy, Feb 13, 2013, 1:04 AM

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This one isn't too hard; just think about it a bit more.

Also a function with a domain and range is a function with a domain and range...you can't assume anything else.

by NewAlbionAcademy, Feb 13, 2013, 1:39 AM

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wait now you're saying C=f(2005) but C=1?

by NewAlbionAcademy, Feb 13, 2013, 5:01 AM

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Plugging in $x=-1$ gives $C=2006$, but then subbing $y=x+2005$ you can get that I believe...

by Binomial-theorem, Feb 13, 2013, 7:34 AM

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Your answer I believe is right, btw where is this PDF you are using lol?

by Binomial-theorem, Feb 13, 2013, 7:36 AM

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