Friday, November 22, 2019

real analysis - What can we conclude from f(x+y)+f(xy)=f(xy)?


Let f:RR be a function such that f(x+y)+f(xy)=f(xy) for all x,yR. Then f is:



A. Strictly increasing.




B. Strictly decreasing.



C. Identically zero.



D. Constant but not necessarily zero.




I have no idea how to do this. Thanks for any hint.

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