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【题目】已知函数fx是定义在R上的偶函数,x≥0时,fx2x23x,则函数fx在R上的解析式是

A.fx=-x2x-3

B.fx=x2|x|-3

C.fx=|x|2x-3

D.fx=|x|2|x|-3

【答案】D

解析∵fx在R上是偶函数,且x≥0时,fx2x23x,

∴当x0时,-x0,f-x2-x23x=2x23x,

则fx=f-x2x23x=-x2x-3

又当x≥0时,fx2x23x=x2x-3,因此fx=|x|2|x|-3

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