Prove that `f(x)gi v e nb yf(x+y)=f(x)+f(y)AAx in R` is an odd function.

If f(x+y)=f(x)*f(y) for all real x,y and f(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^(2)) is an even function.

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

Consider function f(x) satisfies the relation f(x+y^(3))=f(x)+f(y^(3))AAx,yinRand differentiable for all x . Statement I If f'(2)=a then f'(-2)=a f(x) is an odd function.

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)*f(y))f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

Suppose the function f(x) satisfies the relation f(x+y^(3))=f(x)+f(y^(3)).AA x,y in R and is differentiable for all x .Statement 1 If f'(2)=a, then f'(-2)=a Statement 2:f(x) is an odd function.

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

[" Let "f(x+y)=f(x)+f(y)" for all "],[x,y in R" .Then "],[" (A) "f(x)" is an even function "],[" (B) "f(x)" is an odd function "],[" (C) "f(0)=0],[" (D) "f(n)=nf(1),n in N]