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[tex]f(x) = \left\{ \begin{array}{rcl}{-1} & \mbox{if}& -\infty < x < -1, \\ x & \mbox{if} & -1\leq x\leq1, \\1 & \mbox{if} & 1 < x <\infty ,\end{array}\right[/tex]

[tex]g(x) = \frac {1} {2} |x+1 | - \frac {1}{2}|x-1|[/tex]

Prove that [tex]f(x)\equiv g(x)[/tex]

Latex is awesome First time using it here!