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)=`

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

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

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 ……… .

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

If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , then

Statement-1 : A function f : R rarr R satisfies the f(x) - f(y) = x-y, AA x, y in R, f(0), f(1) gt 0 , then f(x) = x+1. and Statement-2 : If function f : R rarr R satisfied the above relationship then f(1) + f(0) + f(3) is equal to 7.

A function f: R -> R satisfy the equation f (x)f(y) - f (xy)= x+y for all x, y in R and f(y) > 0 , then

Consider a differentiable function f:R->R for which f'(0)=ln2 and f(x + y) = 2^x f(y) + 4^y f(x) AA x, y in R which of the following is /are correct?