一类无理函数值域问题的探讨

Some Discussion about the Domain of a Sort of Irrational Functions

双根号类无理函数的值域问题是教学过程中学生比较棘手的问题,在界定该函数的定义域的基础上,采用向量的数量积或三角函数换元法解题,既可减少运算量、便于学生理解与掌握,同时也是促进换位思维、提高学生数学素养的重要途径。

It is a very difficult problem for students how to slove the domain of double square root of irrational functions in teaching. On the base of the domain of definition, we solve some problems by using the dot product of vectors and the substitution method of trigonometric functions, which may reduce the amount of computation and promote transposition thinking. It is also con- venient for students to understand and improve students＇quality.