A function `f: R -> R` satisfy the equation `f (x)f(y) - f (xy)= x+y` for all `x, y in R` and `f(y) > 0`, 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

A function f: RrarrR satisfies the equation f(x) f(y) - f(xy) = x+ y, AAx,y in R and f(1) gt 0 , then

A function f : R to R satisfies the equation f(x + y) = f(x), f(y) for all x, y in R , f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f' (0) = 2. Find (f'(x))/f(x)

A function f:R rarr R satisfy the equation f(x).f(y)=f(x+y) for all x,y in R and f(x)!=0 for any x in R. Let the function be differentiable at x=0 and f'(0)=2, Then : Then :

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

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

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

A function f: R rarr R satisfies the equation f(x+ y)= f(x).f(y) "for all" x, y in R, f(x) ne 0 . Suppose that the function is differentiable at x=0 and f'(0)=2, then prove that f'(x)= 2f(x)