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Math Help - injective function

  1. #1
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    injective function

    Dear all,

    please help me solving this question

    Determine whether the function is injective or surjective.

    f (X) = X3 X
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  2. #2
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    Do you know what the terms mean?

    Injective = For any a and b in the domain, f(a) = f(b) implies a = b. (They map to distinct elements)

    Surjective = For any y in the range, there exists an x such that f(x) = y. (Every element in the range has a corresponding element in the domain)

    Assuming you mean f(x) = x^3 - x then you can factor it and see if the two properties hold.

    Hint: Look at the roots of the polynomial. Also, is this in the reals or the complex?
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  3. #3
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    Quote Originally Posted by zeeshan4u3 View Post
    Dear all,

    please help me solving this question

    Determine whether the function is injective or surjective.


    f (X) = X3 X
    Asked (by a different member it would seem) and answered here: http://www.mathhelpforum.com/math-he...nly-maths.html
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