If `f` be decreasing continuous function satisfying `f(x + y) = f(x) + f(y)-f(x) f(y) Y x, y epsilon R ,f'(0)=1` then `int_0^1 f(x)dx` is

IF f(x+f(y))=f(x)+y AA x, y in R and f(0)=1 , then int_(0)^(10)f(10-x)dx is equal to

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

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

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , 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: R rarr R be a continuous function given by f(x+y)=f(x)+f(y) for all x,y, in R, if int_0^2 f(x)dx=alpha, then int_-2^2 f(x) dx is equal to

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

lf f: R rarr R satisfies, f(x + y) = f(x) + f(y), AA x, y in R and f(1) = 4, then sum_(r=1)^n f(r) is

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to