若f（x+1）为偶函数，则f（x+1）=f（-x+1）还是f（-x-1） 如果f(x+1)为偶函数，则f(x+1)=f(-x+1)，这...
\u82e5f(x+1)\u4e3a\u5076\u51fd\u6570,\u5219f(-x+1)=f(x+1)?\u4e3a\u4ec0\u4e48\u4e0d\u662ff(-x-1)?\u4ee4g\uff08x\uff09=f\uff08x+1\uff09
\u90a3\u4e48f\uff08x+1\uff09\u662f\u5076\u51fd\u6570\uff0c\u8bf4\u660eg\uff08x\uff09\u662f\u5076\u51fd\u6570
\u800cg\uff08x\uff09\u662f\u5076\u51fd\u6570\uff0c\u8bf4\u660eg\uff08-x\uff09=g\uff08x\uff09
\u800cg\uff08-x\uff09=f\uff08-x+1\uff09
\u6240\u4ee5\u662ff\uff08-x+1\uff09=f\uff08x+1\uff09
\u81f3\u4e8ef\uff08-x-1\uff09=f\uff08x+1\uff09
\u5f53x=1\u7684\u65f6\u5019\uff0c\u5f97\u5230f\uff08-2\uff09=f\uff082\uff09
\u5f53x=3\u7684\u65f6\u5019\uff0cf\uff08-4\uff09=f\uff084\uff09
\u7b49\u7b49\u53ef\u77e5\uff0c\u5b8c\u5168\u5c31\u662ff\uff08-x\uff09=f\uff08x\uff09\u7684\u7ed3\u679c\uff0c\u8fd9\u8bf4\u660ef\uff08-x-1\uff09=f\uff08x+1\uff09\uff0c\u5f97\u5230\u7684\u662ff\uff08x\uff09\u662f\u5076\u51fd\u6570\u3002
\u89e3\u8bbeF(x)=f\uff08x+1\uff09
\u7531f(x+1)\u4e3a\u5076\u51fd\u6570
\u5219F(x)\u662f\u5076\u51fd\u6570\uff0c
\u800cF(-x)=f\uff08-x+1\uff09
F(x)=f\uff08x+1\uff09
\u4e14F(-x)=F(x)
\u5373f(x+1)=f(-x+1)
\u6545#\u829d\u9ebb\u5f00\u95e8#\u5982\u679cf(x+1)\u4e3a\u5076\u51fd\u6570\uff0c\u5219f(x+1)=f(-x+1)\uff0c\u8fd9\u662f\u6b63\u786e\u7684\u3002
答案：f(-x-1)
解答过程：令x+1=t
则可得f(t)为偶函数
可得f(t)=f(-t)
即f(x+1)=f[-(x+1)]=f(-x-1)
令x+1=u
因为f(x+1)为偶函数
所以f(u)=f(-u)
所以f(x+1)=f(-x-1)
得f(-x-1) f(x)=f(-x) 整体异号
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