SOLUTION: The function f : R --> R satisfies
f(x) f(y) = f(x + y) + xy for all real numbers x and y. Find all possible functions f.
Algebra.Com
Question 1180033: The function f : R --> R satisfies
f(x) f(y) = f(x + y) + xy for all real numbers x and y. Find all possible functions f.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
See this link
https://math.stackexchange.com/questions/3687605/the-function-f-mathbbr-to-mathbbr-satisfies-fx-fy-fx-y-x
From this link, you may learn that the question was posted to math.stackexchange.com 11 months ago . . .
Since then, it did not obtain any solution/progress and was CLOSED.
Since I visit this site from time to time, I can confirm that their contingent/participants
are prominent, advanced, competent and knowledgeable persons with dynamic minds . . .
RELATED QUESTIONS
The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies
f(x) f(y) - f(xy) = -2x -... (answered by CPhill,ikleyn,greenestamps)
If {{{ f(x+y) = f(x) + f(y) + xy + 1 }}} for all real numbers x and y and {{{ f(1)=1 }}}, (answered by Fombitz)
The function f : \mathbb{R} \rightarrow \mathbb{R} satisfies
xf(x) + f(1 - x)/x = x^3 +... (answered by CPhill)
For all real numbers {{{x}}}, the function {{{f(x)}}} satisfies {{{2f(x) + f(1-x) =... (answered by Edwin McCravy)
If f(x+y)=f(x)+f(y) and f(1)=17, find f(2), f(3), and f(4). Is f(x+y)=f(x)+f(y) for all... (answered by ikleyn)
Let f be a function such that
f(xy) + x = xf(y) + f(x) + xy^2
for all real numbers x... (answered by CPhill,ikleyn,Edwin McCravy,mccravyedwin)
The function f(x) = ax^r satisfies f(2) = 1 and f(32) = 4. Find... (answered by robertb)
If f(x + y) = f(x) + f(y) and f(1) = 3, Find f(2), f(3), and f(4). Is f(x + y) = f(x) + (answered by ikleyn)
The function f(n) is defined for all integers n, such that
f(x) + f(y) = f(x + y) -... (answered by CPhill,ikleyn)