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Functional fiesta (Posted on 2021-08-12)

Find all functions f:R->R such that for all x,y∈R

f(xy + 1) = f(x+y) + f(x)f(y)

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 1 of 3

This turns out to be pretty straightforward,

With x = y = 1 we get

f(2) = f(2) + f(1)^2, so f(1) = 0

with x = y = 0 we get

f(1) = f(0) + f(0)^2 = 0 so f(0) = 0

with y = 0 (and x variable), we get

f(1) = 0 = f(x) + f(x)f(0) = f(x)

Posted by FrankM on 2021-08-12 23:03:58

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