\[\boxed{\text{1151.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[1)\ Пусть\ f(x)\ и\ g(x)\ \]
\[возрастают;\ \ \ x_{1} > x_{2}:\]
\[\left\{ \begin{matrix} f\left( x_{1} \right) > f\left( x_{2} \right) \\ g\left( x_{1} \right) > g\left( x_{2} \right) \\ \end{matrix} \right.\ \Longrightarrow f\left( x_{1} \right) +\]
\[+ g\left( x_{1} \right) > (f\left( x_{2} \right) + g(x_{2})\]
\[\Longrightarrow \varphi\left( x_{1} \right) > \varphi\left( x_{2} \right) \Longrightarrow\]
\[\Longrightarrow возрастает\text{\ φ}(x).\]
\[2)\ \ Пусть\ f(x)\ и\ g(x)\ \]
\[убывают;\ \ \ x_{1} < x_{2}:\]
\[\left\{ \begin{matrix} f\left( x_{1} \right) < f\left( x_{2} \right) \\ g\left( x_{1} \right) < g\left( x_{2} \right) \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow f\left( x_{1} \right) + g\left( x_{1} \right) < (f\left( x_{2} \right) + g(x_{2})\]
\[\Longrightarrow \varphi\left( x_{1} \right) < \varphi\left( x_{2} \right) \Longrightarrow \text{\ φ}(x)\ убывает.\]