Problem 13 - Entrance Test

What is the domain of the function f(x) = √(log(x^2 - 16))?

A. (-∞, -4) ∪ (4, ∞)B. (-∞, -√17] ∪ [√17, ∞)C. (-√17, -4) ∪ (4, √17)D. (-4, 4)

Correct: B

For the square root to be defined, log(x^2 - 16) >= 0. For the logarithm to be defined, x^2 - 16 > 0. x^2 - 16 > 0 => x^2 > 16 => |x| > 4 => x < -4 or x > 4. log(x^2 - 16) >= 0 => x^2 - 16 >= 10^0 => x^2 - 16 >= 1 => x^2 >= 17 => |x| >= √17 => x <= -√17 or x >= √17. Combining these conditions, the domain is (-∞, -√17] ∪ [√17, ∞).