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, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2. Then,

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

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

A function f:R rarr 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 to R satisfies the equation f(x+y) = f (x) f(y), AA x, y in R and f (x) ne 0 for any x in R . Let the function be differentiable at x = 0 and f'(0) = 2. Show that f'(x) = 2 f(x), AA x in R. Hence, determine 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 :

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