How to realize curvate bracket after which two formulas follow in vertical order

Question

I would like to write a equation which defines quantity f(X) to be a if X>0 and b else. I would like to do so writing f(X)= followed by a curvate bracket and then a if x>0 and b else aligned vertically.

By curvate bracket I mean a \bigg version of {.

Answer 1

The cases environment of the amsmath package provides the simplest way to break out a function into different cases. But one can see in the first example that the alignment of the right portion will be affected by the width of what is on the left. Thus, cases supports the use of the alignment tab & to separate and align columns of the case, as shown in the 2nd case.

With the * version of the environment (example 3), which is provided by the mathtools package, the right-hand portion of the case is set as text automatically.

With dcases family of environments, also from the mathtools package, the math is set in \displaystyle automatically (example 4).

As you can see from the comments, there are many environments in the cases family, and one should (myself included) study the documentation to get them all straight.

\documentclass{article}
\usepackage{amsmath,mathtools}
\begin{document}
\[
f(x) = 
\begin{cases}
  a \quad\text{if } x>0\\
  b \quad\text{if } x\le0
\end{cases}
\]
\[
f(x) = 
\begin{cases}
  a & \text{if } x>0\\
  b & \text{if } x\le0
\end{cases}
\]
\[
f(x) = 
\begin{cases*}
 \frac{a}{b}    &  if  $x>0$\\
 b_3  &  for all other situations
\end{cases*}
\]
\[
f(x) = 
\begin{dcases*}
 \frac{a}{b}    &  if  $x>0$\\
 b_3  &  for all other situations
\end{dcases*}
\]
\end{document}