我有一个函数被定义为函数的组合，其中一个是绝对值函数。为了给出它的等效表达式，我也对其进行了分段定义，并在环境中显示了它cases。每个“部分”上的定义都涉及分数，而环境cases没有提供足够的空间。我该如何增加空间？有没有标准的方法来增加这种行间距？
\documentclass[10pt]{amsart}
\begin{document}
\noindent \textbf{1.) }$f(x) = \sqrt{\vert 9 - 2x \vert}$. \\
\hspace*{2em}
\begin{tabular}{r l}
\textbf{i.)} & \hspace*{-0.5em}Is the the graph of $f$ symmetric across a line? \\
\textbf{ii.)} & \hspace*{-0.5em}Is $f$ continuous on $\mathbb{R}$? \\
\textbf{iii.)} & \hspace*{-0.5em}Is $f$ differentiable on $\mathbb{R}$? \\
\end{tabular}
\vskip0.2in
\noindent \textbf{Solution}
\begin{equation*}
f(x) =
\begin{cases}
\sqrt{2\left(\dfrac{9}{2} - x\right)} & \text{if } x \leq \dfrac{9}{2} \\
\sqrt{2\left(x - \dfrac{9}{2}\right)} & \text{if } x \geq \dfrac{9}{2}
\end{cases}
.
\end{equation*}
For every real number $t > 0$,
\begin{equation*}
f\left(\frac{9}{2} + t\right) = \sqrt{2t} = f\left(\frac{9}{2} - t\right) .
\end{equation*}
So, $f$ is symmetric across the vertical line $x = 9/2$.
\end{document}
答案1
dcases从包装中使用mathtools：
\documentclass[10pt]{amsart}
\usepackage{mathtools}
\begin{document}
\noindent \textbf{1.) }$f(x) = \sqrt{\vert 9 - 2x \vert}$. \\
\hspace*{2em}
\begin{tabular}{r@{ }l}
\textbf{i.)} & Is the the graph of $f$ symmetric across a line? \\
\textbf{ii.)} & Is $f$ continuous on $\mathbb{R}$? \\
\textbf{iii.)} & Is $f$ differentiable on $\mathbb{R}$? \\
\end{tabular}
\medskip
\noindent \textbf{Solution}
\begin{equation*}
f(x) =
\begin{dcases}
\sqrt{2\left(\frac{9}{2} - x\right)} & \text{if } x \leq \frac{9}{2}, \\
\sqrt{2\left(x - \frac{9}{2}\right)} & \text{if } x \geq \frac{9}{2}.
\end{dcases}
\end{equation*}
For every real number $t > 0$,
\begin{equation*}
f\left(\frac{9}{2} + t\right) = \sqrt{2t} = f\left(\frac{9}{2} - t\right) .
\end{equation*}
So, $f$ is symmetric across the vertical line $x = 9/2$.
\end{document}
还请注意我所做的其他小调整。
