Writing a nice function

Question

How to write a function mapping like this: MWE

\documentclass{standalone}
\usepackage{amsmath,amssymb}
\begin{document}
$ \begin{matrix} f'\colon & A \to \mathbb{R} \\ & x\mapsto f(x)=x^2 \end{matrix} $
\end{document}

It is not alignment well.

and it must be like

Answer 1

(The following code uses math examples you posted initially.)

Depending on the type of alignment you want, one of the following two solutions may work for you.

\documentclass{article}
\usepackage{array}
\begin{document}

If you want flush-left alignment:
\[
f\colon \begin{array}{>{\displaystyle}l} 
          X \rightarrow Y \\ 
          x\mapsto f(x)=\frac{x-1}{2} 
         \end{array}
\]

\bigskip
If the arrows have to be aligned vertically:
\[
f\colon \begin{array}{>{\displaystyle}r @{} >{{}}c<{{}} @{} >{\displaystyle}l} 
          X &\rightarrow& Y \\ 
          x &\mapsto& f(x)=\frac{x-1}{2} 
         \end{array}
\]
\end{document}

---

Addendum: To align the first row of the array with f\colon, provide the [t] placement option after \begin{array}

\documentclass{article}
\usepackage{array}
\begin{document}
If \verb+f\colon+ should be on the same line as \verb+X\to Y+:
\[
\setlength\arraycolsep{0pt}
f\colon \begin{array}[t]{ >{\displaystyle}r >{{}}c<{{}}  >{\displaystyle}l } 
          X &\to& Y \\ 
          x &\mapsto& f(x)=\frac{x-1}{2} 
         \end{array}
\]
\end{document}