Determine the function satisfying `f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot`

Let f be a differentiable function satisfying f(x+2y)=2yf(x)+xf(y)-3xy+1 AA x , y in R such that f'(0)=1 ,then value of f(8) is equal

Let a real valued function f satisfy f(x+y)=f(x)f(y)AA x,y in R and f(0)!=0 Then g(x)=(f(x))/(1+[f(x)]^(2)) is

If f is a differentiable function satisfying 2f(x)=f(xy)+f((x)/(y)),AA x,y in R^(+), f(1)=0 and f'(1)=(1)/(ln6), then f(7776) =

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(xy)AA x,y in R and if f(2)=5, then find the value of f(f(2))

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' be a fifferentiable real valued function satisfying f (x+2y) =f (x) +f (2y) + 6xy (x+2y) AA x, y in R. Then f ' (0), f" (1), f'(2)….. are in

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=