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 ->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(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(0) is equals a. 1 b. 0 c. -1 d. none of these

Let f(x) be real valued and differentiable function on R such that f(x+y)=(f(x)+f(y))/(1-f(x)dotf(y)) f(x) is Odd function Even function Odd and even function simultaneously Neither even nor odd

Let f: R->R be a twice differentiable function such that f(x+pi)=f(x) and f''(x)+f(x)geq0 for all x in Rdot Show that f(x)geq0 for all x in Rdot

Let f be a differentiable function from R to R such that abs(f(x)-f(y))abs(le2)abs(x-y)^(3//2) ,for all x,y inR .If f(0)=1 ,then int_(0)^(1)f^2(x)dx is equal to

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?

Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot

Let f:(-oo,oo)vec[0,oo) be a continuous function such that f(x+y)=f(x)+f(y)+f(x)f(y),AAx in Rdot Also f'(0)=1. Then [f(2)] equal ([dot] represents the greatest integer function ) 5 b. 6 c. 7 d. 8

A function f:RtoR is such that f(x+y)=f(x).f(y) for all x.y inR and f(x)ne0 for all x inR . If f'(0)=2 then f'(x) is equal to

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot