Math indentation environment

You can also do this with either:

1. the alignat environment along with \matrlap{}, or
2. with the align and use a \hphantom{} to obtain:

---

1. Using \alignat and \mathrlap:

The alignat provides multiple rl align pairs. Since your second alignment is intended to be l aligned, you use a double &&. The first & skips over the r aligned column of the rl align pair.

\mathrlap and related macros are discussed in detail in this TuGboat paper.

Code:

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\begin{alignat*}{3}
    f( & 1 + g( && 2 + \\
       &        && 3), \\
       & \mathrlap{4 + 5 + 6 + 7)}
\end{alignat*}
\end{document}

---

2. Using \align and \hphantom:

You could also just use a \hphantom{} to insert the exact horizontal spacing as is required by its parameter.

Code:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{align*}
    f( & 1 + g( 2 + \\
       & \hphantom{1 + g(} 3), \\
       & 4 + 5 + 6 + 7)
\end{align*}
\end{document}

Yes, it's possible. Use an array for stacking, and drop the intercolumn space, as needed using @{}:

\documentclass{article}
\begin{document}
\[
  \begin{array}{r@{}l@{}l}
    f( & 1 + g( & 2 + \\
       &        & 3), \\
       & \multicolumn{2}{@{}l}{4 + 5 + 6 + 7)}
  \end{array}
\]
\end{document}

If you wish for a more breathable presentation, use \\[\jot] instead of just \\.

\documentclass{article}
\usepackage{mathtools}

\begin{document}

\[
  \begin{array}{ r @{} l @{\mkern\thinmuskip} r }
    f( & 1 + g( & 2 + \\
       &        & 3), \\
       & \mathrlap{4 + 5 + 6 + 7)}
  \end{array}
\]
\end{document}