If a function satisfies `(x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y – InterviewSolution

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1.	If a function satisfies `(x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2`, thenA. f(x) must be polynomial functionB. f(3) = 12C. f(0) = 0D. f(x) may not be differentiable
Answer» Correct Answer - A::B::C `(x-y)f(x+y)-(x+y)f(x-y)=2y(x-y)(x+y)` Let `x-y=u, x+y=v`. Then `uf(v)-vf(u)=uv(v-u)` `rArr" "(f(v))/(v)-(f(u))/(u)=v-u` `rArr" "((f(v))/(x)-v)=((f(u))/(u)-u)=" constant"` `"Let "(f(x))/(x)-x=lambda. " Then"` `f(x)=(lambdax+x^(2))` Since `f(1)=2" then "lambda=1` `therefore" "f(x)=x^(2)+x`

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