Concept:A function is even if f(−x)=f(x) and odd if f(−x)=−f(x).Explanation:Given f(x)=∣x∣−x3.Compute f(−x)=∣−x∣−(−x)3=∣x∣−(−x3)=∣x∣+x3.Compare f(−x) with f(x): ∣x∣+x3=∣x∣−x3 for most x, for example x=1 gives 2=0.Thus f(−x)=f(x), so f is not even.Now compare f(−x) with −f(x)=−∣x∣+x3: ∣x∣+x3=−∣x∣+x3 for non-zero x, e.g., x=1 gives 2=0.Thus f(−x)=−f(x), so f is not odd.Therefore f is neither even nor odd.Answer:Option D: neither even nor odd.