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Describing a function in terms of another

  1. Sep 12, 2008 #1
    1. The problem statement, all variables and given/known data
    I have two functions:

    [tex]
    \begin{array}{l}
    f(x) = \left\{ {\begin{array}{*{20}c}
    {\pi - x\,for\,x \in (0,\pi )} \\
    {0\,for\,x \in (\pi ,2\pi )} \\
    \end{array}} \right. \\
    g(x) = \left\{ {\begin{array}{*{20}c}
    {x\,for\,x \in (0,\pi )} \\
    {0\,for\,x \in (\pi ,2\pi )} \\
    \end{array}} \right. \\
    \end{array}
    [/tex]

    According to my book, then g(x) = f(-x-Pi). But when I insert, I get that g(x) = Pi-(-x-Pi) = 2Pi + x for x € (0, Pi)?
     
  2. jcsd
  3. Sep 12, 2008 #2
    I think it should be g(x) = f(-x + pi). There must have been a typo in the book.

    g(x) = pi - (-x + pi) = pi + x - pi = x.
     
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