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    【题目】已知函数f（x）是定义在R上的偶函数，当x≥0时，f（x）＝2x2－3x，则函数f（x）在R上的解析式是（ ）

    A．f（x）＝－x（2x－3）

    B．f（x）＝x（2|x|－3）

    C．f（x）＝|x|（2x－3）

    D．f（x）＝|x|（2|x|－3）

    【答案】D

    【解析】∵f（x）在R上是偶函数，且x≥0时，f（x）＝2x2－3x，

    ∴当x＜0时，－x＞0，f（－x）＝2（－x）2＋3x＝2x2＋3x，

    则f（x）＝f（－x）＝2x2＋3x＝－x（－2x－3）．

    又当x≥0时，f（x）＝2x2－3x＝x（2x－3），因此f（x）＝|x|（2|x|－3）．

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