f(x)=根号下( 4-log0.5(4-x平方) )的定义域怎么求

Question

主要是log0.5(4-x²)的值域怎么求不会..

Answer 1

4-log0.5(4-x²)≥0且4-x²>0
log0.5(4-x²)≤4=log(0.5)0.5^4=log(0.5)1/16且4-x²>0
4-x²≥1/16且4-x²>0
-3√7/4≤x≤3√7/4且-2＜x＜2
∴-3√7/4≤x≤3√7/4
定义域:[-3√7/4,3√7/4]

Answer 2

题意得
4-log0.5 (4-x²)≥0
4-x²>0
∴-3√7/8≤x≤3√7/8
----------------------------注：
4-x²>0∴-2<x<2
∵4-log0.5 (4-x²)≥0∴og0.5(4-x²)≤4∴4-x²≥0.5^4=1/16∴x²≤63/64∴-3√7/8≤x≤3√7/8