• 若x∈R,n∈N*,定义:Mxn=x(x+1)(x+2)…(x+n-1),例如M3-5=(-5)?(-4)(-3)=-60,则函数f(x)=M7x-3cos20052006x( )试题及答案-单选题-云返教育

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      若x∈R,n∈N*,定义:Mxn=x(x+1)(x+2)…(x+n-1),例如M3-5=(-5)?(-4)(-3)=-60,则函数f(x)=M7x-3cos
      2005
      2006
      x(  )

      试题解答


      B
      解:由题意可得,f(x)=(x-3)(x-2)(x-1)x(x+1)(x+2)(x+3)cos
      2005
      2006
      x
      =x(x
      2-9)(x2-4)(x2-1)cos
      2005
      2006
      x
      ∴f(-x)=-x(x
      2-9)(x2-4)(x2-1)cos(-
      2005
      2006
      x)
      =-x(x
      2-9)(x2-4)(x2-1)cos
      2005
      2006
      x=-f(x)
      ∴函数f(x)为奇函数
      故选:B
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