Concept:Use the substitution x=sinθ and the identity sin3θ=3sinθ−4sin3θ.Explanation:Let x=sinθ.Since x∈[−1/2,1/2], we get θ∈[−π/6,π/6].Now, 3x−4x3=3sinθ−4sin3θ=sin3θ.So, y=3sin−1(sinθ)+sin−1(sin3θ).Because θ∈[−π/6,π/6], we have 3θ∈[−π/2,π/2].Thus, sin−1(sinθ)=θ and sin−1(sin3θ)=3θ.Therefore, y=3θ+3θ=6θ.Since θ∈[−π/6,π/6], multiplying by 6 gives 6θ∈[−π,π].Hence, y∈[−π,π].Answer:−π≤y≤π, which is option A.