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Math Help - Proving coordinate functions

  1. #1
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    Proving coordinate functions

    Given that f: l --> R is a coordinate function for l.

    Prove that g: l --> R defined by g(P) = f(P) + c for some constant c is also a coordinate function for l.

    My textbook defines coordinate function as one that is both one-to-one and "onto" such that PQ = |f(P) - f(Q)|

    I already figured out how to prove the one-to-one, but I'm having issues with proving the "onto" part of it. In class, my professor just said it was a matter of "adding c and subtracting c," but I couldn't figure out what he meant by that. Any ideas?
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  2. #2
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    Quote Originally Posted by spectralsea View Post
    Given that f: l --> R is a coordinate function for l. Prove that g: l --> R defined by g(P) = f(P) + c for some constant c is also a coordinate function for l.
    I'm having issues with proving the "onto" part of it.
    ONTO
    \begin{gathered}<br />
  x \in R \Rightarrow x - c \in R \hfill \\<br />
  \left( {\exists P \in I} \right)\left[ {f(P) = x - c} \right] ~,f\text{ is onto}\hfill \\<br />
  g(P) = f(P) + c = \left( {x - c} \right) + c = x \hfill \\ <br />
\end{gathered}
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  3. #3
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    Awesome, thank you. So in general, if you were trying to prove a function was onto, you would start out with x being a real number and then trying to work it out so that some f(P) would bring you back to the x you started with?
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  4. #4
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    Quote Originally Posted by spectralsea View Post
    So in general, if you were trying to prove a function was onto, you would start out with x being a real number and then trying to work it out so that some f(P) would bring you back to the x you started with?
    In general yes. But in this case we knew that f is onto and we need to prove that g is also.
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