I would not use an aligned approach in an inline set. Here is something your can work with:
\documentclass{memoir}
\usepackage{amsmath}
\begin{document}
Let us consider the function
\begin{align*}
f\colon A &\to A,\\
x &\mapsto \big(f_1(x), f_2(x)\big).
\end{align*}
Saepe at quas accusamus molestiae possimus consequatur vitae.
For an inline attempt, I would go with
$f\colon A \to A,\, x \mapsto \big(f_1(x), f_2(x)\big)$.
Saepe at quas accusamus molestiae possimus consequatur vitae.
\end{document}

Seriously, you should consider some basic training in TeX, for example https://ctan.org/pkg/lshort-english, https://ctan.org/pkg/short-math-guide or https://ctan.org/pkg/latex-amsmath.