\documentclass{article}

\usepackage{amsmath}

\begin{document}

\[
  f(x) =
    \begin{cases}
      1    & \text{if } x \in U \\
      F(x) & \text{if } x \notin U.
    \end{cases}
\]
If~$T$ is open in $[0,1]$ then
\[
  f^{-1}[T] =
    \begin{cases}
      \big(F^{-1}[T] \cap X \big)\cup U & \text{if } 1 \in T \\
      F^{-1}[T] \cap V                  & \text{if } 1 \notin T,
    \end{cases}
\]

\end{document}