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问题 解答题

已知定义在R上的奇函数f（x）的图象经过点（2，2），且当x∈（0，+∞）时，f（x）=loga（x+2）．

（1）求a的值；

（2）求函数f（x）的解析式．

答案

（1）∵函数f（x）的图象经过点（2，2），

∴f（2）=loga（2+2）=2，∴a=2．

（2）∵函数f（x）为奇函数，∴f（0）=0．

∵当x∈（0，+∞）时，f（x）=loga（x+2），

则当x∈（-∞，0）时，-x∈（0，+∞），

∴f（x）=-f（-x）=-log2（2-x）．

综上可得，f(x)=

log2(x+2)，x＞0
0，x=0
-log2(2-x)，x＜0
．

填空题

缺词填空 。

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