Re: ISI 2011

Posted by Abhitesh on Dec 06, 2016; 7:55am
URL: http://discussion-forum.276.s1.nabble.com/ISI-2011-tp7602954p7602964.html

xf(x) + 2f(-x) = -1 holds for all x --- eq(1)

Thus -xf(-x) + 2f(x) = -1
Multiplying by x

-x^2.f(-x) + 2xf(x) = -x   --- eq(2)

2*eq(1) - eq(2) gives (4+x^2)f(-x) = -2+x
=> f(-x) = x-2/(4+x^2)
=> f(x) = (-x-2)/(4+x^2)

which is the only function to satisfy given equation.