Let `f: R^+ ->R` be a function which satisfies `f(x)dotf(y)=f(x y)+2(1/x+1/y+1)` for `x , y > 0.` Then find `f(x)dot`

Let be a real function satisfying f(x)+f(y)=f((x+y)/(1-xy)) for all x ,y in R and xy ne1 . Then f(x) is

Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) for all x ,\ y > 0. If f^(prime)(1)=1 then find f(x)dot

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

Let f:R rarr R be a function which satisfies f(x+y)=f(x)+f(y) AA x, y in R . If f(1)=2 and g(n)=sum_(k-1)^((n-1))f(k),n in N then the value of n , for which g(n)=20 , is :

If f:RtoR is a function which satisfies the condition f(x)+f(y)=f((x+y)/(1+xy)) for all x, y in R except xy=-1 , then range of f(x) is

Let f:R rarr R be a function satisfying condition f(x+y^(3))=f(x)+[f(y)]^(3) for all x,y in R If f'(0)>=0, find f(10)

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1_ =a. Then , f (x) =

Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in R. If f (x) is differentiable at x = 0, then

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^(2)y-y^(3))AA x,y in R and f(1)=2 ,then