若函数y=log2(x^2-2)的值域为[1,log2(4)],其定义域为

题目

若函数y=log2(x^2-2)的值域为[1,log2(4)],其定义域为

答案

1 ≤ log2(x² - 2) ≤ log2(4)
log2(2) ≤ log2(x² - 2) ≤ log2(4)
2 ≤ x² - 2 ≤ 4
4 ≤ x² ≤ 6
-√6 ≤ x ≤ -2 或 2 ≤ x ≤ √6