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Math test question

  1. Sep 27, 2004 #1
  2. jcsd
  3. Sep 28, 2004 #2
    Like Jasonrox I don't know what you mean I would advise you making
    it very clear exactly what the question says because it does not look
    anything like any other question I have seen teaching at uni or school.

    is F(-2) = 1, F(-1) =-2 ,F(0)=0,F(1) =-1. F(2)=2 ?

    If you have something like F(x)=F(y) when x is not y
    then the function is not one to one.
    eg if F(-1) = 2 and F(2)=2 then the function F is not one to one.

    the comment about odd functions is a common question I have taught at uni and school if f(x) = x^3 then f(-x) = -f(x) so x^3 is odd and symmetrical about the origin.
    Last edited: Sep 28, 2004
  4. Sep 28, 2004 #3


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    Staff Emeritus
    Science Advisor

    A function is NOT "one-to-one" if f(x)= f(y) for different x and y.
    A function is "symmetric about the origin" if f(-x)= -f(x) (A line drawn through the points (x, f(x)) and (-x,-f(x)) has the origin at its center).

    I'm not crazy about problems where you are asked to decide something like that given only some of the values (strictly speaking that's impossible!) but assuming that the values given are sufficient, I note that G(-2)= 3= G(2) so G is NOT one to one. Also, H(-2)= 1 and H(2)= -1, H(-1)= -3 and H(1)= 3 so, at least for the values shown, H is symmetric about the origin.
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