Determine all functions `f: R->R` such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1 `AAx , ygeq0 in Rdot`

Determine all functions f: Rvecs u c ht h a tf(x-f(y))=f(f(y))+xf(y)+f(x)-1AAx , ygeq in Rdot

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)=

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

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:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f(a-y)+f(y)f(a-x), forall x,y in R , then for some real a,

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f be a differentiable function from R to R such that |f(x) - f(y) | le 2|x-y|^(3/2), for all x, y in R . If f(0) =1, then int_(0)^(1) f^(2)(x) dx is equal to

If f:R rarr R satisfying f(x-f(y))=f(f(y))+xf(y)+f(x)-1, for all x,y in R , then (-f(10))/7 is ……… .