基本初等函数的连续性是基本初等函数的重要性质,现行的很多数学分析教材都对基本初等函数的连续性给出了证明.我们发现不少教材在用ε-δ定义证明指数函数、对数函数的连续性时,实质上使用了[1]中p50-51的定理2.12.我们将此定理原文引述如下:定理2.12设y=f(x)在区间[a,b]上严格单调增加,f(a)=α,f(b)=β,则它的反函数x=f-1(y)在区间[α,β]上连续且严格单调增加.证明由定理2.1知x=f-1(y)在区间[α, The continuity of basic elementary functions is an important property of basic elementary functions, and many current mathematical analysis materials prove the continuity of elementary elementary functions. We find that many textbooks prove the exponential function with the definition of ε-δ, logarithm Theorem 2.12 of p50-51 in [1] is essentially used for the continuity of the function. Theorem 2.12 Let y = f (x) be strictly monotonically increasing in the interval [a, b] The inverse function x = f-1 (y) of a is continuous and strictly monotonically increasing in the interval [α, β] when f (a) = α and f 1 (y) in the interval [α,