题目内容
若函数![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_ST/0.png)
A.-1
B.1
C.
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_ST/1.png)
D.
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_ST/2.png)
【答案】分析:根据若函数
是奇函数,得到f(-x)=-f(x),代入函数解析式,得到恒成立的方程,整理对应相等,即可求得常数a的值.
解答:解:∵函数
是奇函数,
∴
=![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/3.png)
即
=![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/5.png)
解得a=
.
故选D.
点评:考查函数的奇偶性的定义,以及方程的思想方法求参数的值,特别注意函数的定义域,属中档题.
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/0.png)
解答:解:∵函数
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/1.png)
∴
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/3.png)
即
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/5.png)
解得a=
![](http://thumb.1010pic.com/pic6/res/gzsx/web/STSource/20131103172628232948880/SYS201311031726282329488008_DA/6.png)
故选D.
点评:考查函数的奇偶性的定义,以及方程的思想方法求参数的值,特别注意函数的定义域,属中档题.
![](http://thumb2018.1010pic.com/images/loading.gif)
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