The 0 you're talking about is just a member of the domain of f. (And what is f anyway?) This has nothing to do with the zero vector of F(ℝ). You really need to look at the definition of F(ℝ).Well at the point where the function touches the y axes so x=0, then no matter what the sign is both f(x)=f(-x)= the same thing. So does it mean that the vertex point at the origin satisfies this?
I also second micromass' recommendation that you should try to think of a few examples of members of F(ℝ), just to make sure that you know what sort of things are considered "vectors" in this problem.