We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
42
2
avatar+153 

Let S be the set of all nonzero real numbers. Let f : S to S be a function such that f(x) + f(y) = f(xyf(x +  y)) for all x, y in S such that x + y \(\neq\) 0. Let n be the number of possible values of f(4), and let s be the sum of all possible values of f(4). Find n * s.

 Nov 23, 2019
 #1
avatar
0

Taking x = y = 0, you get 2f(0) = f(0), so f(0) = 0.

 

Taking y = 0, you get f(x) + f(0) = f(0) = 0, so f(x) = 0.


So the only function is f(x) = 0, and n*s = 1*0 = 0.

 Nov 24, 2019
 #2
avatar+153 
0

The answer is to be in the form of a fraction so 0 is unreasonable.

AoPS.Morrisville  Nov 24, 2019

30 Online Users

avatar
avatar
avatar