A function `f(x)` is so defined that for all real `x,{f(x)}^n = f(nx).` Prove that `f(x) · f '(nx) = f'(x) · f(nx).`

A function f is defined such that for all real x,y(a)f(x+y)=f(x).f(y)(b)f(x)=1+xg(x) where lim_(x rarr0)g(x)=1 prove that f;(x)=f(x) and f(x)=e^(x)

If (f(x))^(n) = f(nx) , find (f'(nx))/(f'(x)) .

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

Given a differentiable function f(x) defined for all real x, and is such that f(x+h)-f(x)<=6h^(2) for all real h and x . Show that f(x) is constant.

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

The f(x) is such that f(x+y) = f(x) + f(y) , for all reals x and y xx then f(0) =