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18 February, 17:42

Is it possible for an odd function to have the interval 0 infinity) as its domain?

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Answers (2)
  1. 18 February, 19:58
    0
    NO!

    Prove by contradiction. First, define the the following terms:

    odd function: f (-x) = - f (x) ] and domain: all values of x

    Proof: Suppose there f (-x) = - f (x) such that x is a negative integer, then f (-x) is a positive number ( - (-x) = + x) and - f (x) is a negative number (negative of a positive number is a negative number). Since a positive number cannot equal a negative number, then this is not possible.

    Answer: No
  2. 18 February, 21:17
    0
    Answer with Step-by-step explanation:

    Yes, it is possible for an odd function to have the interval 0 to infinity as its domain.

    Let f (x) = - x

    f (-x) = - (-x)

    = x

    and - f (x) = - (-x)

    = x

    Clearly, f (-x) = - f (x)

    Hence, f (x) = - x is an odd function.

    and clearly the domain of f (x) = - x is the set of all real numbers which also contains the interval (0,∞)

    Hence, it is possible for an odd function to have the interval 0 to infinity as its domain.
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