\documentclass[12pt]{article}

\begin{document}

$$
\begin{array}{lcl}
f(r) = 1.0 &\mathrm{for}& r < r_m \\
f(r) = (1 - x)^3*(1+3x+6x^2) &\mathrm{for}& r_m < r < r_{cut} \\
f(r) = 0.0 &\mathrm{for}& r >= r_{cut} \\
\end{array}
$$

\end{document}