Let f be any function defined on R and let it satisfy the condition :
`| f (x) - f(x) | le ( x-y)^2, AA (x,y) in R ` if ` f(0) =1, ` then :

A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y), AA x, y in R . If f'(0) = - 1, then

Let |f (x)| le sin ^(2) x, AA x in R, then

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

Let f be a differentiable function defined on R such that f(0) = -3 . If f'(x) le 5 for all x then

Let f be an even function defined on R. Suppose f is defined on [0,4] as follows: f(x) = {{:(3x, if, 0 le x lt 1),(4-x, if, 1 le x le 4):} and f satisfies the condition. f(x-2) = f{x + [(6x^(2) + 272)/(x^(2) + 2)]) AA x in R Where [x] = greatest integer le x . Then f(3271) +f(-2052) + f(806) =..............

Let f(x+y)-axy=f(x)+by^(2),AA x,y in R,f(1)=8,f(2)=32 , then a+b=?