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\begin{exercise}
On suppose qu'une fonction num\'{e}rique $f$ v\'{e}rifie : $f(x)\geq
0\Rightarrow x\geq-1$. D\'{e}terminer si les affirmations suivantes  sont
vraies ou fausse en expliquant votre r\'{e}ponse. 

\begin{enumerate}


\item Les solutions de l'in\'{e}quation $f(x)\geq0$ sont  $[-1\,;\,+\infty[$. 

\item On note $\mathcal{S}$ l'ensemble des solutions de  l'in\'{e}quation
$f(x)\geq0$. 

\begin{enumerate}


\item Si $x\in\mathcal{S}$ alors $x\in[-1\,;\,+\infty[$. 

\item Si $x\in[-1\,;\,+\infty[$ alors $x\in\mathcal{S}$. 
\end{enumerate}

\item Si $x\in]-\infty\,;\,-1[$ alors $f(x)<0$. 

\item Si $f(x)<0$ alors $x\in]-\infty\,;\,-1[$. 

\item Si $x\geq-1$ alors $f(x)$ existe. 
\end{enumerate}
\end{exercise}


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