ISI 2011

[Addy-2]

CONTENTS DELETED

The author has deleted this message.

[Abhitesh]

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.