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Math Help - discrete math function

  1. #1
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    discrete math function

    determine whether the function f(x)^2-3(x)+1 is one-to-one, onto, or both. Prove your answer. The domain and codomain if f(x) is the set of all real numbers.

    f(x) = 3x^2 -3x + 1

    the function is onto Y, but not one-to-one:

    because 1 is a real number and

    f(1) = 3(1)^2-3(1)+1 = 1

    and 0 is a real number

    f(0) = 3(0)^2-3(0)+1 = 1

    there exists two different elements in x that map to a single element in y; therefore, f is not one-to-one.

    the function is onto Y, since all real numbers of Y coexist with all real numbers of X.



    OK, my question is did I correctly prove that

    1. the function is one-to-one?

    2. how do I prove the last one is true algebraically?

    I assume its true since the domain is (-00, 00) and range is(-00, 00)?

    thanks!
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  2. #2
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    Quote Originally Posted by robasc View Post
    determine whether the function f(x)^2-3(x)+1 is one-to-one, onto, or both. Prove your answer. The domain and codomain if f(x) is the set of all real numbers.

    f(x) = 3x^2 -3x + 1

    the function is onto Y, but not one-to-one:

    because 1 is a real number and

    f(1) = 3(1)^2-3(1)+1 = 1

    and 0 is a real number

    f(0) = 3(0)^2-3(0)+1 = 1

    there exists two different elements in x that map to a single element in y; therefore, f is not one-to-one.

    the function is onto Y, since all real numbers of Y coexist with all real numbers of X.


    "Coexist"? That is not a mahtematical term. The function is not onto the real numbers, not even close: that quadratic's

    discriminant is \Delta=3^2-4\cdot 3\cdot 1=-3<0 , and this means the function is always positive or always negative...

    Tonio




    OK, my question is did I correctly prove that

    1. the function is one-to-one?

    2. how do I prove the last one is true algebraically?

    I assume its true since the domain is (-00, 00) and range is(-00, 00)?

    thanks!
    .
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  3. #3
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    I see now since this is a parabola it does not even map to any negative values in y, but i am not following the discriminant ?

    I do not think I am familiar with discriminant. I am a serious newbie at this stuff.

    please explain how to do this?
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