If `f(x+y)=f(x)dotf(y)` for all real `x , ya n df(0)!=0,` then prove that the function `g(x)=(f(x))/(1+{f(x)}^2)` is an even function.

If f(x+y)=f(x)*f(y) for all real x,y and f(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^(2)) is an even function.

If f(x+y)=f(x).f(y) for all real x,y and f(0)!=0, then the function g(x)=(f(x))/(1+{f(x)}^(2)) is:

If f (x+ y ) = f (x) . F(y) for all real x,y and f(0 ) ne 0 then the funtions g (x) = ( f(x) )/( 1+ { f(x) }^(2)) is

Let f(x+y)=f(x)*f(y)AA x,y in R and f(0)!=0* Then the function phi defined by .Then the function phi(x)=(f(x))/(1+(f(x))^(2)) is

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)

Let f be a real function. Prove that f(x)-f(-x) is an odd function and f(x)+f(-x) is an even function.

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dxdot

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) .