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Homework Help: Triangle Inequality Q

  1. Aug 19, 2011 #1
    1. The problem statement, all variables and given/known data

    Part of an [itex]\epsilon-\delta[/itex] proof about whether or not f + 2g is continuous at x = a provided that f and g are continuous at x = a

    3. The attempt at a solution

    I've got the proof (I hope), but I'm uncertain about whether I can do the following:

    [itex]|f(x)+2g(x)-(f(a)+2g(a))| = |f(x)-f(a)+2g(x)-2g(a)| \leq |f(x)-f(a)| + 2|g(x)-g(a)|[/itex] using the triangle inequality.

    Is that valid?

    Thanks!!
     
  2. jcsd
  3. Aug 19, 2011 #2

    vela

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    Sure. Why not?
     
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