【答案】
分析:根據(jù)使表達(dá)式有意義,列出相關(guān)的不等式式組即可.
(1)函數(shù)有意義,根號(hào)下非負(fù),對(duì)數(shù)式的真數(shù)大于0;
(2)先根據(jù)真數(shù)大于0轉(zhuǎn)化為絕對(duì)值不等式,再分類(lèi)討論解絕對(duì)值不等式,
解答:解:(1)欲使其有意義,只須
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/0.png)
解得
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/1.png)
故得x∈[-5,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/2.png)
)∪(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/3.png)
)∪(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/4.png)
,5]
(2)欲使其有意義,只須2|cosx|-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/5.png)
sinx-cosx>0 (*)
當(dāng)cosx>0時(shí),(*)可變?yōu)閏osx-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/6.png)
sinx>0即cos(x+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/7.png)
)>0,又0≤x<π,所以
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/8.png)
<x+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/9.png)
<
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/10.png)
故x∈[0,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/11.png)
)
當(dāng)cosx<0時(shí),(*)可變?yōu)?3cosx-
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/12.png)
sinx>0,即
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/13.png)
cosx+sinx<0,可轉(zhuǎn)化為sin(x+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/14.png)
)<0
又0≤x<π,所以π<x+
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/15.png)
<
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/16.png)
,故x∈(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/17.png)
,π)
故其定義域?yàn)閤∈[0,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/18.png)
)∪(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/19.png)
,π)
答:
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/20.png)
的定義域是[-5,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/21.png)
)∪(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/22.png)
)∪(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/23.png)
,5]
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/24.png)
的定義域是[0,
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/25.png)
)∪(
![](http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131023214546323109654/SYS201310232145463231096018_DA/26.png)
,π)
點(diǎn)評(píng):考查函數(shù)定義域的求法,其理論依據(jù)是使得函數(shù)有意義.