$\displaystyle f(x)=xf(x)$
$\displaystyle
(x-1)f(x)=0
$
Put $\displaystyle x=2$,which gives $\displaystyle f(2)=0$
Someone should prove that $\displaystyle f(1)=0$ if the answer is indeed $\displaystyle f(1)$
Will you tell me the source of this question
the problem is that
f{x} = x f{x}
so, whatever value u put for X, the inequality will never ever hold.
lets take an example x = 2
f{2} = 2* f{2}
1 = 2 (inequality doesnt hold)
f{3} = 3* f{3}
1= 3 {inequality doesnt hold)
the inequality holds IFF f(x) = 0. but,
f(1) = 1 . f{1}
so , f{1} can / cannot be 0. but we cant say for sure.
(have Pmed u the source of the question)