perplexus.info :: Just Math : Functional fiesta

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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re(2): Solution - problem

Comment 3 of 3 |

(In reply to re: Solution - problem by Brian Smith)

This branch at least suggests one addition function:

f(x) = - delta(0,x)

where delta is the Kronecker delta function...

Later, never mind: this fails when x = -1/y

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

Fails, giving incorrectly:

-1 = 0 + (0)(0)

Edited on August 13, 2021, 6:39 pm

Posted by Steven Lord on 2021-08-13 11:04:35

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