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`, then

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then (a) f(x) is an even function (b) f(x) is an odd function (c) If f(2)=a ,then f(-2)=a (d) If f(4)=b ,then f(-4)=-b

Let f:R to R be a function satisfying f(x+y)=f(x)=lambdaxy+3x^(2)y^(2)"for all "x,y in R If f(3)=4 and f(5)=52, then f'(x) is equal to

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x+1)),AAx > -1. If f(0)=5, then f(x) is

Find function f(x) which is differentiable and satisfy the relation f(x+y)=f(x)+f(y)+(e^(x)-1)(e^(y)-1)AA x, y in R, and f'(0)=2.

Let f: R^+ ->R be a function which satisfies f(x)dotf(y)=f(x y)+2(1/x+1/y+1) for x , y > 0. Then find f(x)dot

If a function f: R ->R be such that f(x-f(y)) = f(f(y) )+xf(y)+f(x) -1 AA x , y in R then f(2)=

A function f: RvecR satisfies the equation f(x)f(y)-f(x y)=x+yAAx ,y in Ra n df(1)>0 , then f(x)f^(-1)(x)=x^2-4 b. f(x)f^(-1)(x)=x^2-6 c. f(x)f^(-1)(x)=x^2-1 d. none of these