2010年全国高中联赛江西省预赛题第3题:函数f(x)=(1-2x)~(1/2)/(x+2)的值域是.这是一道求无理函数值域的题目,看上去并不复杂,但其中蕴含着诸多的数学思想方法,本文给出几种解法,敬请各位读者指正.思路一三角代换法分析由于函数解析式中含有(1-x2)~(1/2),让人联想到三角公式,于是可采用三角换元法.解法1易知函数的定义域为[-1,1]. 2010 National High School League in Jiangxi province preliminary question the third question: the function f (x) = (1-2x) ~ (1/2) / (x +2) the value of the field is a seek unreasonable function range Problem, it seems not complicated, but it contains a lot of mathematical thinking and methods, this article gives several solutions, please readers correct me thinking a triangle substitution method analysis as the function contains (1-x2) ~ (1/2), reminiscent of the trigonometric formula, so triangular trigonometry can be used. Solution 1 The domain of easy-to-know function is [-1,1].