[f(x)]^2,这是奇函数还是偶函数? f=2^x是奇函数还是偶函数
f(x)=x^2-x\u662f\u5947\u51fd\u6570\u8fd8\u662f\u5076\u51fd\u6570\uff1f\u8981\u8be6\u7ec6\u7684\u8fc7\u7a0b(x)=x^2-x\u662f\u975e\u5947\u975e\u5076\u51fd\u6570\uff0c\u56e0\u4e3a\u5b83\u4e0d\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0c\u800c\u4ed6\u7684\u5bf9\u79f0\u8f74\u4e5f\u4e3ax=1/2\uff0c\u4e0d\u662fy\u8f74\u3002
\u8fd9\u4e2a\u51fd\u6570\u5728(-\u221e,+\u221e)\u662f\u5355\u589e\u51fd\u6570,\u56e0\u6b64\u975e\u5947\u975e\u5076
\u56fe\u50cf\uff1a
\u5982\u679c\u5bf9\u4e8e\u51fd\u6570f(x)\u7684\u5b9a\u4e49\u57df\u5185\u7684\u4efb\u610f\u4e00\u4e2ax\u503c\uff0c\u90fd\u6709f(\uff0dx)=\uff0df(x)\uff0e\u90a3\u4e48\u5c31\u79f0f(x)\u4e3a\u5947\u51fd\u6570\u3002\u5982\u679c\u5bf9\u4e8e\u51fd\u6570f(x)\u7684\u5b9a\u4e49\u57df\u5185\u7684\u4efb\u610f\u4e00\u4e2ax\u503c\uff0c\u90fd\u6709f(\uff0dx)=f(x)\uff0c\u90a3\u4e48\u5c31\u79f0f(x)\u4e3a\u5076\u6570\u3002
因为对于定义域内的任意x,有[f(-x)]^=[±f(x)]^=[f(x)]^
否则是非奇非偶函数.如令f(x)为指数函数,[f(x)]^还是一个指数函数.
非奇非偶函数
设f(x)=2x-3
[f(x)]^2=(2x-3)^2
是一条关于直线x=3/2对称的抛物线
奇函数必须关于原点对称
偶函数必须关于y轴对称
不一定的,
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