用初等方法求函数值域，一般来说是相当困难的，需用很多特殊的技巧，且只能解决一些特殊的问题，本文将运用微积分的方法对初等函数的值域作一般的讨论．一、介值定理的推广我们知道，对闭区间上的连续函数有介值定理：若ｆ（ｘ）在区间［ａ，ｂ］上连续，ｆ（ａ）＝Ａ，... It is generally very difficult to find the value range of the function by the elementary method. It requires a lot of special techniques and can only solve some special problems. This article will discuss the range of the elementary functions by calculus in general. First, the promotion of the theorem of the intermediation We know that there is a value theorem for the continuous function on a closed interval: f (a) = A, if f (x) is continuous in the interval [a, b]