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 f:R->R be a function such that f(x+y)=f(x)+f(y),AA x, y in R.

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

A continuous function f(x)onR->R satisfies the relation f(x)+f(2x+y)+5x y=f(3x-y)+2x^2+1forAAx ,y in R Then find f(x)dot

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

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

A function f : R→R satisfies the equation f(x)f(y) - f(xy) = x + y ∀ x, y ∈ R and f (1)>0 , then

Consider f: R^(+)->R such that f(3)=1 for a in R^+ a n d """"f(x)dotf(y)+ f(3/x)f(3/y)=2f(x y)AAx ,y in R^+dot Then find f(x)dot

Consider f: R^+vecRs u c ht h a tf(3)=1 for a in R^+a n df(x)dotf(y)+f(3/x)f(3/y)=2f(x y)AAx ,y in R^+dot Then find f(x)dot

If a real valued function f(x) satisfies the equation f(x +y)=f(x)+f (y) for all x,y in R then f(x) is