1) Based on the information obtainable from the graph in Figure 2, show, with appropriate reasoning, that the function: $$f ( x ) = \sqrt { 2 } - \frac { e ^ { x } + e ^ { - x } } { 2 } \quad x \in \mathbb { R }$$ adequately represents the profile of the platform for $x \in [ - a ; a ]$; also determine the value of the endpoints $a$ and $-a$ of the interval.
Ministry of Education, University and Research
To visualize the complete profile of the platform on which the bicycle will be able to move, several copies of the graph of the function $f(x)$ relating to the interval $[-a; a]$ are placed side by side, as shown in Figure 3. [Figure] Figure 3
1) Based on the information obtainable from the graph in Figure 2, show, with appropriate reasoning, that the function:
$$f ( x ) = \sqrt { 2 } - \frac { e ^ { x } + e ^ { - x } } { 2 } \quad x \in \mathbb { R }$$
adequately represents the profile of the platform for $x \in [ - a ; a ]$; also determine the value of the endpoints $a$ and $-a$ of the interval.
\section*{Ministry of Education, University and Research}
To visualize the complete profile of the platform on which the bicycle will be able to move, several copies of the graph of the function $f(x)$ relating to the interval $[-a; a]$ are placed side by side, as shown in Figure 3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{4247a904-6fcc-4fd2-a50f-9c2a64781d61-2_477_1121_561_479}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}