f（x）为偶函数，则f（x-2）=f（2-x）吗？求证明
\u8bbe\u51fd\u6570f(x)=x2-2|x|-1(-3\u2264x\u22643) (1)\u8bc1\u660ef(x)\u662f\u5076\u51fd\u6570\u5e94\u8be5\u662f\u8bbe\u51fd\u6570f(x)=x²-|2x|-1(-3\u2264x\u22643\uff09\u8bc1\u660ef(x)\u662f\u5076\u51fd\u6570
\u9996\u5148\uff0c\u5b9a\u4e49\u57df\u5173\u4e8e\u539f\u70b9\u5bf9\u79f0\uff0c
\u5176\u6b21\uff0c\u5229\u7528f(-x)=-f(x)\u8bc1\u660e
f(-x)=(-x)²-|-2x|-1=x²-|2x|-1=f(x)
\u6240\u4ee5\u539f\u51fd\u6570\u662f\u5076\u51fd\u6570
\u9898\u76ee\u6709\u8bef\uff0c\u5e94\u8be5\u662f\u8bc1\u660ef'(0)=0
\uff1d\uff1d\uff1d\uff1d\uff1d\uff1d\uff1d
\u8bc1\u660e\uff1a
\u56e0\u4e3af(x)\u662f\u5076\u51fd\u6570\uff0c\u6240\u4ee5\u4e00\u5b9a\u6ee1\u8db3\u5173\u7cfb
f(-x)=f(x)
\u82e5f'(x)\u5b58\u5728\uff0c\u5bf9\u4e0a\u9762\u7684\u7b49\u5f0f\u4e24\u8fb9\u6c42\u5bfc\u5f97
[f(-x)]'=f'(x)
-f'(-x)=f'(x)
\u4ee4x=0\u65f6\uff0c-f'(0)=f'(0)
\u6240\u4ee5f(0)=0
您好！偶函数有个性质f（x）为偶函数，则f（x）=f（-x）！你令x=x-2
根据偶函数定义：
f(-X)=f(X)，
∴f(2-X)=f［-(X-2)］=f(X-2)。
因为是偶函数，所以f（x）=f（-x）
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