2. 外语
  3. Which of the following functions f defined for all numbers x has the property that f(-x)=-f(x) for all numbers x?

Which of the following functions f defined for all numbers x has the property that f(-x)=-f(x) for all numbers x?

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问题 Which of the following functions f defined for all numbers x has the property that f(-x)=-f(x) for all numbers x?
选项 A、f(x) = x3/(x2+1)
B、f(x) =(x2-1)/(x2+1)
C、f(x) = (x2-1)x2
D、f(x) = (x3-1)x
E、f(x) = (x3-1)x2
答案A
解析 选项A:

f(-x)=-f(x)，A正确。
选项B:

f(-x)≠-f(x)。
选项C：f(-x)=[(-x)2-1](-x)2=(x2-1)x2；-f(x)=-(x2-1)x2；f(-x)≠-f(x)。
选项D：f(-x)=f[(-x)2-1)(-x)=(x3+1)x；-f(x)=-(x3-1)x；f(-x)≠-f(x)。
选项E：f(-x)=[(-x)2-1)(-x)2=(-x3-1)x2；-f(x)=-(x3-1)x2；f(-x)≠-f(x)。
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