Answer: [-5, 1].
- A [-5, 1]
- B [-3, 1]
- C [-5, -1]
- D (-5, 1)
Correct answer: A. [-5, 1]
Explanation: For the outer square root, we need log(2 - log(x²+4x+5)) >= 0, which requires 2 - log(x²+4x+5) >= 1, i.e. log(x²+4x+5) <= 1. (The inner log is always defined since x²+4x+5 > 0 for all x, its discriminant being negative.) So x²+4x+5 <= 10, giving x²+4x-5 <= 0, (x+5)(x-1) <= 0, so x is in [-5, 1].
Concept context
Ordered pairs, Cartesian products, types of relations and functions, domain and range. Foundation for calculus and Class 12 algebra.