题目内容
16.若函数f(x+1)=x2-2x+1,则函数f(x)的解析式为f(x)=(x-2)2.分析 将f(x+1)=x2-2x+1变形,令x=x+1替换即可.
解答 解:∵f(x+1)
=x2-2x+1
=x2+2x+1-4(x+1)+4
=(x+1)2-4(x+1)+4,
∴f(x)=x2-4x+4=(x-2)2.
点评 本题考查了求函数的解析式问题,考查转化思想,是一道基础题.
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