Let \( \mathbb{R} \) denote the set of all real numbers. Let \( f : \mathbb{R} \to \mathbb{R} \) be an arbitrary function and let \( g : \mathbb{R} \to \mathbb{R} \) be the function defined by \( g(x) = x f(x) \), for all \( x \in \mathbb{R} \).
Then which of the following statements is (are) TRUE?
