Question Detail
Question
The solution of \( |x^2 - 1| < 1 \) is:
Correct Answer
Option A is the correct answer.
Detailed Explanation
|x² - 1| < 1 implies -1 < x² - 1 < 1. Adding 1: 0 < x² < 2. Taking the square root (considering positive values): |x| < √2 and x ≠ 0 (since x² > 0). So the solution is -√2 < x < √2, excluding x=0. However, option A is -√2 < x < √2, which is the same set. Option B is incorrect because x=0 satisfies |0-1|=1 which is not less than 1.
Hint
Solve the compound inequality: -1 < x² - 1 < 1. Then isolate x² and take square roots.