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Math Help - Injective function

  1. #1
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    Injective function

    Hi,

    How do I prove that this functions is injective?

    a.) f : x --> x + x x ∈ R
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  2. #2
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    Quote Originally Posted by Hellbent View Post
    Hi,

    How do I prove that this functions is injective?

    a.) f : x --> x + x x ∈ R
    Assume f(x) = f(y) for some x,y \in \mathbb{R}

    Then, x+x^3 = y+y^3. You need to finish the proof by showing that x=y.
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  3. #3
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    Quote Originally Posted by Defunkt View Post
    Assume f(x) = f(y) for some x,y \in \mathbb{R}

    Then, x+x^3 = y+y^3. You need to finish the proof by showing that x=y.
    That's the problem I have.

    f(a) = a + a, f(b) = b + b
    f(a) = f(b) => a + a = b + b => a = b
    => a = b
    therefore f is one-to-one
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