Math Environment

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
$$
f(x) = \left\{\begin{array}{rlr}
-1, & \text{for} & x \leq  0\\
+1, & \text{for} & x > 0\\
\end{array}\right\} \qquad x \in \mathbb{N}
$$

$$
f(x) = \left\{\begin{array}{rlr}
-1, & \text{for} & x \leq  0\\
+1, & \text{for} & x > 0\\
\end{array}\right. \qquad x \in \mathbb{N}
$$
\end{document}