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

Which of the following functions/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/defined for all numbers x has the property that f(-x)= -f(x)for all numbers x ?
选项 A、
B、
C、f(x)= x2(x2-1)
D、f(x)= x(x3-1)
E、f(x)=x2(x3-1)
答案A
解析 To determine which of the functions among the five choices has the property that f(-x)= -f(x)for all numbers x, you need to check each choice until you find one that has the property. In Choice A, f(x)=:

Therefore Choice A has the property f(-x)= -f(x), and since only one of the five choices can be the correct answer, the correct answer is Choice A.
This explanation uses the following strategies.
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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