For a function `f(x), f(0) = 0` and `f'(x)=1/(1+x^2)` , prove that `f(x)+f(y)= f ((x+y)/(1-xy))`

If f (x) = log_e ((1+x)/(1-x)) , prove that: f (x) +f (y)= f ((x+y)/(1+xy)) .

If f(x) = log_e ((1-x)/(1+x)) , then prove that f(x) + f(y) = f((x + y)/(1 + xy))

If f(x) = (x-1)/(x+1) , then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/(1+xy) .

If f(x)=cos(logx) ,show that f(x)f(y)-1/2 [ f (x/y) + f(xy) ]=0

A function f:R rarr R satisfies that equation f(x+y)=f(x)f(y) for all x,y in R ,f(x)!=0. suppose that the function f(x) is differentiable at x=0 and f'(0)=2. Prove that f'(x)=2f(x)

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

A function f: R->R satisfies that equation f(x+y)=f(x)f(y) for all x ,\ y in R , f(x)!=0 . Suppose that the function f(x) is differentiable at x=0 and f^(prime)(0)=2 . Prove that f^(prime)(x)=2\ f(x) .

If f(x) is a function such that f(xy)=f(x)+f(y) and f(3)=1 then f(x) =

If f(x)=cos(log x), then f(x)f(y)-(1)/(2)[f((x)/(y))+f(xy)]=

If f(x)=cos(log x), then f(x)f(y)-(1)/(2)[f((x)/(y))+f(xy)]=