对于求形如y=m(ax+b)～(1/2)+n(cx+d)～(1/2)(其中mn≠0,ac<0)的无理函数的最值(值域)的问题,本文旨在对此进行求法探究及其推广.第一种类型:当mn<0时,形如y=m(ax+b)～(1/2)+n (cx+d)～(1/2)(其中ac<0)直接利用函数的单调性求最值(或值域)例如(2010年全国高中数学联赛第1题) For the most value (range) of the irrational function of the form y = m (ax + b) ~ (1/2) + n (cx + d) ~ (1/2) where mn ≠ 0, ), The purpose of this article is to explore and promote its method of seeking. The first type: when mn <0, the shape is y = m (ax + b) ~ (1/2) + n (cx + d) ~ (1/2) (where ac <0) directly use the monotonicity of the function to find the most value (or range) for example (2010 National High School Math Champions League title 1)