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\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 1315865105268--
%%--Fonctions composées--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}
\begin{enumerate}
\item Soient $f$, $g$ et $h$ les fonctions définies par%
\[
\ f(x)=2/x,\quad g(x)=x^{2}\quad\text{et}\quad h(x)=3x+1.
\]


Calculer $(f\circ g)(x)$, $(g\circ f)(x),$ $(h\circ g)(x),$ $(g\circ h)(x),$
$(h\circ f)(x),$ $(f\circ h)(x)$ et déterminer leur domaine de définition.

\item Soient $f$, $g$ et $h$ les fonctions définies par:%
\[
f(x)=\sin(3x+1),\quad g(x)=3\sin x+1,\quad h(x)=\sin x^{2},\quad i(x)=\sin
^{2}x.
\]


Décomposer $f$, $g,$ $h$ et $i$ à l'aide de fonctions usuelles.$\medskip$
\end{enumerate}
\end{exercise}

\begin{exercise}
$\vspace*{-0.35cm}$

\begin{enumerate}
\item À l'aide d'une décomposition en deux fonctions usuelles, déterminer les
variations des fonctions suivantes:%
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\begin{enumerate}
\item $f(x)=-2x^{2}+4;$

\item $g(x)=(-2x+4)^{2};$

\item $h(x)=\sin(\pi-3x)\quad$sur $[0;2\pi/3].$
\end{enumerate}

%

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\item Déterminer les variations de $f:x\mapsto\dfrac{1}{x-1}$ et \textbf{en
déduire} celles de $g:x\mapsto\dfrac{1}{x-1}-x.$
\end{enumerate}
\end{exercise}


\end{document}