Describing a function in terms of another

[Niles]

Homework Statement

I have two functions:

$$\begin{array}{l}<br /> f(x) = \left\{ {\begin{array}{*{20}c}<br /> {\pi - x\,for\,x \in (0,\pi )} \\<br /> {0\,for\,x \in (\pi ,2\pi )} \\<br /> \end{array}} \right. \\ <br /> g(x) = \left\{ {\begin{array}{*{20}c}<br /> {x\,for\,x \in (0,\pi )} \\<br /> {0\,for\,x \in (\pi ,2\pi )} \\<br /> \end{array}} \right. \\ <br /> \end{array}$$

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)?

 

[steelphantom]

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.