教材中的定理: ||a|-|b||≤|a±b|≤|a|+|b|,也称为“三角形不等式”,由此容易得到|a+b|≥||a|-|b||,|a+b|≤|a|+|b|,|a-b|≥||a|-|b||,|a-b|≤|a|+|b|,取等号的充要条件分别是ab≤0,ab≥0,ab≤0,ab≤0. 利用这些规律解题,常会带来很多方便. 1.求值域例1 函数y=x+1/x的值域. 解因为 Theorem in the textbook: ||a|-|b||≤|a±b|≤|a|+|b|, also known as the “triangle inequality”, so it is easy to get |a+b|≥||a |-|b||,|a+b|≤|a|+|b|,|ab|≥||a|-|b||,|ab|≤|a|+|b|, equal sign The necessary and sufficient conditions are ab ≤ 0, ab ≥ 0, ab ≤ 0, and ab ≤ 0. Using these laws to solve problems often brings a lot of convenience. 1. Evaluating domain example 1 function y=x+1/x Value range. Solution because