If f : R to R such that f(x- f(y)) = f...

If `f : R to R `such that ` f(x- f(y)) = f( f(y) ) + x f (y) +f(x) - 1 AA , y in R ` then f(x) is

A

`1+ (x^(2))/(4)`

B

`1- (x^(2))/(2)`

C

`1+ (x^(2))/(2)`

D

`1-(x^(2))/(4)`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

If f : R to R is continuous such that f(x + y) = f(x) + f(y) x in R , y in R and f(1) = 2 then f(100) =

Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x, y in R . If f (x) is differentiable every where and f '(0) =1, find f '(x).

If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=

If f : R to R is defined as f (x+ y) = f (x) + f (y) AA x, y in R and f (1) = 7, then find sum _(r =1) ^(n) f (r).

If f(x)+2f(1-x)=x^(2)+2 AA x in R , then f(x) is given by

If f(x) is a function such that f(x+y)=f(x)f(y) and f(5) =125 " then " f(x)=

If f(x+y) = f(x)f(y) and f(5)=32 then f(7)=