If I have a modular expression of type:
\begin{equation}\nonumber
w(c)=-\frac{\pi}{2}\frac{\left|-1+c\right|(1+c)+\left|1+c\right|(-1+c)}{(1-c^2)}
\end{equation}
How can I express the solutions to $w$ in terms of $c$, with conditions on the intervals where c can be?
I know I should analyze four possible situations, using the fact that,
\begin{equation}\nonumber
|x| =
\begin{cases}
x,& \text{if $x>0$} \\
-x, & \text{if $x\le0$}
\end{cases}
\end{equation}
After making such an analysis, in two of them we have $w=0$, and in the last two we have $w=\pi\text{ e }w=-\pi$.
However, I have not yet been able to define $w$ in terms of the intervals over the variable $c$. In this case I know that $w$ is a type of peacewise function.
Thank you in advance.
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D.Silva
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but you have written $$w=w(c)$$ or what do you mean? – Dr. Sonnhard Graubner Feb 23 '18 at 18:38
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Compute the function for $c<-1$,$-1<c<1$, and $1<c$. – user Feb 23 '18 at 20:14
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In this case. Is it correct says that, $w(-1<c<1)=w(-1<c<0)+w(0<c<1)$? – D.Silva Feb 26 '18 at 11:47