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Math Help - Functions

  1. #1
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    Functions

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    Why is the following assertion false? "If f(2)=2 and f(4)=4, then f(3)=3."
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    this is that last problem on one of my homeworks. I think it is a trick question and that it is actually true...but i am not sure. please help, thanks.
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  2. #2
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    Quote Originally Posted by talhaguy View Post
    ___________________
    Why is the following assertion false? "If f(2)=2 and f(4)=4, then f(3)=3."
    ___________________

    this is that last problem on one of my homeworks. I think it is a trick question and that it is actually true...but i am not sure. please help, thanks.
    It is sometimes true.
    Consider,
    f(x)=x.

    It is false when you consider
    f(x)=x+(x-2)(x-4)
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  3. #3
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    Hello, talhaguy!

    Why is the following assertion false?
    "If f(2)=2 and f(4)=4, then f(3)=3."

    All we know about the function are two points: (2,2),\:(4,4)

    The graph could look like this:
    Code:
          |
          |                *
          |             *     *(4,4)
          |           *       :
          |          *        :
          |                   :
          |    (2,2)*         :
          |         :         :
          |         :         :
          |         :         :
         -+---------+----+----+------
          |         2    3    4

    That is, f(3) could be anywhere on the line x = 3.

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  4. #4
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    thankyou so much guys, i really appreciate it.
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