How to remove the unwanted vertical space?

Question

I'm using Exam class to create solutions, but the flaign* environment does not align my equation with the \part. How do I make them align?

\documentclass[a4paper, twoside, 12pt]{exam}

\usepackage{amssymb,amsmath}
\usepackage{graphicx}
\marksnotpoints
\pointsinrightmargin 
\bracketedpoints
\printanswers

\begin{document}
\begin{questions}

\question  The functions $f$ and $g$ are defined by 
\begin{align*}
f : x &\mapsto 4-x^2, \ \ x \in \mathbb{R} \\ 
g : x &\mapsto \frac{1}{x-4}, \ \ x\in \mathbb{R}, \ x \not= 4.
\end{align*}
\begin{parts}
   \part[3] Define $f\circ g$ in a similar form.
\end{parts}

\begin{solution}
\begin{parts}
    \part 
        \begin{flalign*}
            fg(x) &= f(g(x)) &\\ 
            &=f(\frac{1}{x-4}) \\ 
            &= 4 - \frac{1}{(x-4)^2}
        \end{flalign*}
\end{parts}
\end{solution}

Specifically, my problem is here in this image:

Answer 1

This might be a good application for TABstacks, which can be placed inline, unlike align environments.

\documentclass[a4paper, twoside, 12pt]{exam}

\usepackage{amssymb,amsmath}
\usepackage{tabstackengine}
\stackMath
\setstackgap{S}{5pt}% GAP BETWEEN ADJACENT STACKED EQUATION ROWS
\usepackage{graphicx}
\marksnotpoints
\pointsinrightmargin 
\bracketedpoints
\printanswers

\begin{document}
\begin{questions}

\question  The functions $f$ and $g$ are defined by 
\begin{align*}
f : x &\mapsto 4-x^2, \ \ x \in \mathbb{R} \\ 
g : x &\mapsto \frac{1}{x-4}, \ \ x\in \mathbb{R}, \ x \not= 4.
\end{align*}
\begin{parts}
   \part[3] Define $f\circ g$ in a similar form.
\end{parts}

\begin{solution}
\begin{parts}
    \part 
        \alignShortunderstack{
            fg(x) =& f(g(x)) \\ 
            =&f(\dfrac{1}{x-4}) \\ 
            =& 4 - \dfrac{1}{(x-4)^2}
        }
\end{parts}
\end{solution}
\end{questions}
\end{document} 

If one always wants to process TABstack arguments in \displaystyle, this undocumented code can be added to the preamble

\makeatletter
\renewcommand\TAB@delim[1]{\displaystyle#1}
\makeatother

Answer 2

You have to use inline math here. Maybe like the following:

% arara: pdflatex

\documentclass[a4paper, twoside, 12pt]{exam}
\usepackage{amssymb,mathtools}
\marksnotpoints
\pointsinrightmargin 
\bracketedpoints
\printanswers

\begin{document}
    \begin{questions}       
        \question  The functions $f$ and $g$ are defined by 
        \begin{alignat*}{2}
        f : x &\mapsto 4-x^2,  &&\quad x\in \mathbb{R} \\ 
        g : x &\mapsto \frac{1}{x-4}, &&\quad x\in \mathbb{R} \vee x \not= 4.
        \end{alignat*}
        \begin{parts}
            \setcounter{partno}{2} % for demo only
            \part[3] Define $f\circ g$ in a similar form.
        \end{parts}
        \begin{solution}
            \begin{parts}
            \setcounter{partno}{2} % for demo only
                \part 
                $\!\begin{aligned}[t]
                f(x)\circ g(x) &= f(g(x)) &\\ 
                &= f\Bigl(\frac{1}{x-4}\Bigr) \\ 
                &= 4 - \frac{1}{(x-4)^2}
                \end{aligned}$
            \end{parts}
        \end{solution}  
\end{questions} 
\end{document}