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

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)=

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

Let f be a function such that f(x+f(y))=f(f(x))+f(y) forall x, y in R and f(h)=h for 0 where epsilon >0 , then determine f'(x) and f(x).

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,

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) is a differentiable function on x in R , such that f(x+y)=f(x)f(y) for all x, y in R where f(0) ne 0 . If f(5)=10, f'(0)=0 , then the value of f'(5) is equal to

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

If f:R rarr (0,oo) be a differentiable function f(x) satisfying f(x+y)-f(x-y)=f(x)*{f(y)-f(y)-y}, AA x, y in R, (f(y)!= f(-y) " for all " y in R) and f'(0)=2010 . Now, answer the following questions. Which of the following is true for f(x)