初等函數(shù)值域的若干求法

黃星　張倩瑤

摘 要 函數(shù)的值域是由全體函數(shù)值所構(gòu)成的集合，它取決于函數(shù)的定義域和對應(yīng)法則.求函數(shù)的值域涉及各種數(shù)學(xué)思想方法和代數(shù)式的變形技巧.本文主要介紹了基本初等函數(shù)法、分離常數(shù)法、基本不等式法、配方法、單調(diào)性法、判別式法、換元法、反解法、導(dǎo)數(shù)法和圖像法等常見的求初等函數(shù)值域的方法.

關(guān)鍵詞 初等函數(shù) 值域

中圖分類號(hào)：G633.6 文獻(xiàn)標(biāo)識(shí)碼：A DOI：10.16400/j.cnki.kjdkx.2019.02.023

Abstract The range of a function is a set of all its values， which depends on its definition and corresponding rules. The range of a function involves various mathematical methods and algebraic deformations. This paper mainly introduces the basic elementary function method， separation constant method， basic inequality method， formula method， monotonicity method， discriminant method， substitution method， inverse method， derivative method and image method and other common methods for finding the range of elementary functions.

Keywords elementary function； range

參考文獻(xiàn)

[1] 華東師范大學(xué)數(shù)學(xué)系.數(shù)學(xué)分析[M].北京：高等教育出版社，2010.

[2] 同濟(jì)大學(xué)數(shù)學(xué)系.高等數(shù)學(xué)[M].北京：高等教育出版社，2007.