f(x)" satisfies the equation "f(x+1)+f(x-1)=sqrt(3)f(x)" for "x in R" then which is correct "

The function f(x) satisfies the equation f(x+1)+f(x-1)=sqrt(3)f(x) .then the period of f(x) is

The function f(x) satisfies the equation f(x + 1) + f(x-1) = sqrt3 f(x) . then the period of f(x) is

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

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

Let f(x) be a differentiable function satisfying the equation f'(x)=-f(x)f(-x) and f(0)=(1)/(2) ,then which is/are correct?

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

The function f (x) satisfy the equation f (1-x)+ 2f (x) =3x AA x in R, then f (0)=

f(x) satisfies the equation (x-1)f((x+1)/(x-1))-f(x)=x,AA x!=1 Find all such functions.