A continuous function `f(x)onRvec` satisfies the relation `f(x)+f(2x+y)+5x y=f(3x-y)+2x^2+1forAAx ,y in RdotT h e nfin df(x)dot`

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 a continuous function f(x) on R rarr R be defined such that it satisfies the relation f(x)+f(x+2y)+3xy=2f(2y-x)+2y^(2)AA x,y in R Then which of the following is true

If f satisfies the relation f(x+y)+f(x-y)=2f(x)f(y)AA x,y in K and f(0)!=0; then f(10)-f(-10)-

If a real valued function f(x) satisfies the equation f(x+y)=f(x)+f(y) for all x,y in R then f(x) is

If the function f(x) satisfies the relation f(x+y)=y(|x-1|)/((x-1))f(x)+f(y) with f(1)=2. then lim_(x rarr1)f'(x) is

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

A discontinuous function y=f(x) satisfying x^(2)+y^(2)=4 is given by f(x)=...

let f(x) be the polynomial function. It satisfies the equation 2 +f(x)* f(y) = f(x) + f(y) +f(xy) for all x and y. If f(2) =5 find f|f(2)| .

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.