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f(x)f(y) = f(x+y) + xy

 

I need to find all possible functions f

 

I have tried some substitutions such as x = y = 0

 

f(0)f(0) = f(0) + 0

so f(0) = 0 or f(0) = 1

 

Then let x = 0

 

f(0)f(y) = f(y)

 

I think this implies that f(0) has to be 1.

 

Not sure where to go from here.

 May 27, 2020
 #1
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You should check if f(x) = x works.

 May 27, 2020
 #2
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you should check for x=1 and y=1.

 May 28, 2020

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