Let E₁ = {x ∈ ℝ : x ≠ 1 and x/(x − 1) > 0} and E₂ = {x ∈ E₁ : sin⁻¹(logₑ(x/(x − 1))) is a real number}. (Here, the inverse trigonometric function sin⁻¹x assumes values in [−π/2, π/2].) Let f : E₁ → ℝ be the function defined by f(x) = logₑ(x/(x − 1)) and g : E₂ → ℝ be the function defined by g(x) = sin⁻¹(logₑ(x/(x − 1))). LIST-I: P. The range of f is; Q. The range of g contains; R. The domain of f contains; S. The domain of g is. LIST-II: 1. (−∞, 1/(1 − e)] ∪ [e/(e − 1), ∞); 2. (0, 1); 3. [−1/2, 1/2]; 4. (−∞, 0) ∪ (0, ∞); 5. (−∞, e/(e − 1)]; 6. (−∞, 0) ∪ (1/2, e/(e − 1)]. The correct option is: