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)=`

If a function f:R rarr R be such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1AA x,y in R then f(2)=

Determine all functions f:R rarr R such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1quad AA x,y>=0in R

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 a function f:R rarr R be such that f(1)=2 , f'(0) = ln2 and f(x+y)=2^(x)f(y)+4^(y)f(x),AA x,y in R . If f'(2)=k ln2 ,then number of divisors of k ,is

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 a function f:R rarr R such that f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x)AA x,y in R . If f'(2)=kln2 ,then the value of k is

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

Let f be a polynominal such that f(x) f(y) + 2 = f(x) + f(y) + f(xy) AA xx, y in R (0) and f(x) is one one AA xx in R with f(0) = 1 and f (1) = 2 The function y = f(x) is given by