For the function to be defined, the expression under the square root must be non-negative: (x + 5) / (x² - 9) ≥ 0. Factor the denominator: (x + 5) / [(x - 3)(x + 3)] ≥ 0. The critical points are -5, -3, and 3. Testing intervals: 1) x > 3: Positive. 2) -3 < x < 3: Negative. 3) -5 ≤ x < -3: Positive. 4) x < -5: Negative. Since we need the result to be ≥ 0, we select the positive intervals. Note that x = -3 and x = 3 must be excluded because they result in division by zero (hence open brackets), while x = -5 is included because the numerator can be zero (hence a closed bracket). This leads to x ∈ [-5, -3) ∪ (3, ∞). Option 2 represents the intervals where the expression is negative. Option 3 and 4 are mathematically incomplete or ignore the critical points of the numerator.