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Math Help - Real Analysis Help!!

  1. #1
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    Real Analysis Help!!

    This one has been bothering me for days now. Can anyone help??

    Show that if f is continuous and f(0) = 1, f(1) = e, and f(x + y) = f(x)f(y) then f(x) = e^x.
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  2. #2
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    Quote Originally Posted by mathprincess24 View Post
    This one has been bothering me for days now. Can anyone help??

    Show that if f is continuous and f(0) = 1, f(1) = e, and f(x + y) = f(x)f(y) then f(x) = e^x.
    See this.
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  3. #3
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    how do i know that f(x) = e^x?
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    Quote Originally Posted by mathprincess24 View Post
    how do i know that f(x) = e^x?
    From the "initial conditions" i.e. f(0)=1 and f(1)=e.
    Do you see how?
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  5. #5
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    yes i understand that when you plug in e^x as the function that all the conditions are met, but how do i prove that its the only one that works. I'm not sure i understand the proof on the bottom half of the link you responded with.
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