perplexus.info :: Just Math : Functional Equation

Functional Equation (Posted on 2020-12-22)

Find all funtions f:R->R such that f(xy-1)+f(x)f(y)=2xy-1 for all reals x and y.

No Solution Yet Submitted by Danish Ahmed Khan

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re: Solution?

Comment 2 of 2 |

(In reply to Solution? by Larry)

I agree f(0) needs to be 0. But then from (1,1): f(0) + f(1)^2 = 1, couldn't f(1)=-1?

Then f(1) + f(1)*f(2) = 3 makes f(2)=-4, and then f(2)+f(1)f(3) = 5 makes f(3)=-9, ...

So then f(x) = -x^2 also looks like a solution.

Posted by Brian Smith on 2020-12-23 21:23:43

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