ISI 2011 PEA MATH

[saumya singha]

Q-
The number of continuous functions f satisfying
X F(Y) + Y F(X)= (X+Y)F(X) F(Y) , where x and y are any real
numbers, is

A.1
B.2
C.3
D.NONE

HOW DO WE SOLVE THIS?

[leon]

hi saumya, what you can do is substitute x=0 and y=y.
You'll get the answer as f(x)=0 or f(x)=1.
Ans is option b.