$\begin{array}{l}
c)y = \sqrt {\left( {m + 1} \right){x^2} - 2\left( {m - 1} \right)x + 3m - 3} \\
HS\,xd\,tren\,R \Leftrightarrow \left( {m + 1} \right){x^2} - 2\left( {m - 1} \right)x + 3m - 3 \ge 0,\forall x \in R\\
\Leftrightarrow \left\{ \begin{array}{l}
m + 1 > 0\\
\Delta ' = {\left( {m - 1} \right)^2} - \left( {m + 1} \right)\left( {3m - 3} \right) \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m > - 1\\
\left( {m - 1} \right)\left( {m - 1 - 3m - 3} \right) \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m > - 1\\
\left( {m - 1} \right)\left( { - 2m - 4} \right) \le 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m > - 1\\
\left( {m - 1} \right)\left( {2m + 4} \right) \ge 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
m > - 1\\
m \ge 1;m \le - 2
\end{array} \right. \Leftrightarrow m \ge 1
\end{array}$
