`f(x)+f(y)=f((x+y)/(1-xy))` ,for all`x,yinR`.`(xy!=1)`,and `lim_(x->0) f(x)/x=2`.Find`f(1/sqrt3)`and `f'(1)`.

"If "f(x)+f(y)=f((x+y)/(1-xy))" for all "x,y in R, (xyne1), and lim_(xrarr0) (f(x))/(x)=2" then find "f((1)/(sqrt(3))) and f'(1).

If f(x)+f(y)=f((x+y)/(1-xy))x>y in R,xy!=1,lim_(x rarr0)(f(x))/(x)=2. Find f(5),f'(-2)

If f(x) + f(y) = f((x+y)/(1-xy)) for all x, y in R (xy ne 1) and lim_(x rarr 0) (f(x))/(x) = 2 , then

If f(x+y)=f(x)+f(y) -xy -1 for all x, y in R and f(1)=1 then f(n)=n, n in N is true if

f(x+(1)/(y))+f(x-(1)/(y))=2f(x)*f((1)/(y)) for all xy in R-{0} and f(0)=(1)/(2), then f(4) is

Let f(x)=(1)/(2)[f(xy)+f((x)/(y))] for x,y in R^(+) such that f(1)=0f'(1)=2

Let f(x+y)=f(x)+f(y)+x^2y+y^2x and lim_(x rarr 0)(f(x))/x=1 . Find f'(3) .

If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1, then find the value of lim_(x->0)(2^(f(tan x)-2^f(sin x)))/(x^2*f(sin x))

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