find all the function $f,g:R\rightarrow R$ such that (1)for every $x,y\in R$ we have $f(xg(y+1))+y=xf(y)+f(x+g(y))$ (2)$f(0)+g(0)=0$
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Tags: function, algebra
guangzhou-2015
20.06.2017 07:37
This problem has been posted before
dilraba
20.06.2017 10:33
guangzhou-2015 wrote: This problem has been posted before Has this problem been solved? Can you show me the previous post?
Tintarn
20.06.2017 10:43
dilraba wrote: Has this problem been solved? Can you show me the previous post? Please don't hesitate to make your own use of the search function. Type in (for instance) "f(xg(y+1))" and you will immediately find at least three appearences of this problem with complete solutions from 2010, 2015, 2016.
I'm sorry not providing you the direct link to this result but I encountered users who never tried the search function, thinking quite easier to have other users make the search for them. So now I prefer to point to the search function and to give the appropriate search term (I checked that it indeed will give you the expected result) instead of the link itself (wink)