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The function $$f : \mathbb{R} \to \mathbb{R}$$ satisfies $$f(x) f(y) = f(x + y) + xy$$ for all real numbers x and y. Find all possible functions f.

I tried subsituting in simple values for x and y, but nothing works. A full explanation would be appreciated, as I am really confused! Thank you so much!

Oct 24, 2021

#1
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I checked if there were constant solutions, and there are none, so I don't think there are any other solutions.

Oct 24, 2021
#2
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I have no idea how to solve this, but I did find this. I hope this helps. :))

Let x = 0

f(0)*f(y) = f(y) + 0

f(0) = 1

=^._.^=

Oct 25, 2021
#3
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I do not know how to do it either but I would be interested in seeing the answer.

Oct 25, 2021