Question

6．求函數(shù)f（x）=$\frac{\sqrt{x+5}}{lg（6-{x}^{2}）}$的定義域．

Answer 1

分析 要使函數(shù)f（x）=$\frac{\sqrt{x+5}}{lg（6-{x}^{2}）}$有意義，則被開(kāi)方數(shù)大于等于0，同時(shí)對(duì)數(shù)的真數(shù)大于0且分式的分母不等于0，列出不等式組，求出x的范圍即為定義域．

解答 解：要使函數(shù)f（x）=$\frac{\sqrt{x+5}}{lg（6-{x}^{2}）}$有意義，
則$\left\{\begin{array}{l}{x+5≥0}\\{6-{x}^{2}＞0}\\{lg（6-{x}^{2}）≠0}\end{array}\right.$，
解得：$-\sqrt{6}＜x＜-\sqrt{5}$或$-\sqrt{5}＜x＜\sqrt{5}$或$\sqrt{5}＜x＜\sqrt{6}$．
故函數(shù)f（x）=$\frac{\sqrt{x+5}}{lg（6-{x}^{2}）}$的定義域?yàn)椋海?-\sqrt{6}$，$-\sqrt{5}$）∪（$-\sqrt{5}$，$\sqrt{5}$）∪（$\sqrt{5}$，$\sqrt{6}$）．

點(diǎn)評(píng) 本題考查求函數(shù)的定義域需要開(kāi)偶次方根的被開(kāi)方數(shù)大于等于0，對(duì)數(shù)的真數(shù)大于0且分式的分母不等于0，是基礎(chǔ)題．