`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)`.

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N such that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Let f(x) be defined for all x > 0 and be continuous. Let f(x) satisfy f((4x)/y)=f(x)-f(y) for all x,y and f(4e) = 1, then (a) f(x) = In 4x(b) f(x) is bounded (c) lim_(x->0) f(1/x)=0 (d) lim_(x->0)xf(x)=0

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) f(x)

Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x^(2)y+xy^(2) for all real numbers x and y. If lim_(xrarr0) (f(x))/(x)=1, then The value of f'(3) is

f:R^+ ->R is a continuous function satisfying f(x/y)=f(x)-f(y) AAx,y in R^+ .If f'(1)=1,then (a)f is unbounded (b) lim_(x->0)f(1/x)=0 (c) lim_(x->0)f(1+x)/x=1 (d) lim_(x->0)x.f(x)=0