Question

20．函數(shù)y=$\frac{{\sqrt{x+1}}}{x}$+ln（2-x）的定義域是{x|-1≤x＜0或0＜x＜2}．

Answer 1

分析 根據(jù)函數(shù)成立的條件即可求函數(shù)的定義域．

解答 解：要使函數(shù)有意義，則$\left\{\begin{array}{l}{x＞0}\\{x+1≥0}\\{2-x＞0}\end{array}\right.$，
即$\left\{\begin{array}{l}{x≠0}\\{x+1≥0}\\{2-x＞0}\end{array}\right.$，
則$\left\{\begin{array}{l}{x≠0}\\{x≥-1}\\{x＜2}\end{array}\right.$，
即-1≤x＜0或0＜x＜2，
故函數(shù)的定義域?yàn)閧x|-1≤x＜0或0＜x＜2}．
故答案為：{x|-1≤x＜0或0＜x＜2}

點(diǎn)評(píng) 本題主要考查函數(shù)的定義域的求解，要求熟練掌握常見(jiàn)函數(shù)成立的條件．