Đáp án: 60 B; 61.A
Giải thích các bước giải:
$\begin{array}{l}
60)\\
y = f\left( {1 + {x^2}} \right)\\
\Rightarrow y' = 2x.f'\left( {1 + {x^2}} \right) < 0\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x < 0\\
f'\left( {1 + {x^2}} \right) > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
x > 0\\
f'\left( {1 + {x^2}} \right) < 0
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x < 0\\
\left[ \begin{array}{l}
1 + {x^2} > 4\\
1 + {x^2} < 2
\end{array} \right.
\end{array} \right.\\
\left\{ \begin{array}{l}
x > 0\\
2 < 1 + {x^2} < 4
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x < - \sqrt 3 \\
- 1 < x < 0\\
1 < x < \sqrt 3
\end{array} \right.\\
\Rightarrow B\\
61)\\
y = {\left( {f\left( x \right)} \right)^2}\\
\Rightarrow y' = 2f'\left( x \right).f\left( x \right) < 0\left( 1 \right)\\
Do:f\left( 2 \right) = f\left( { - 2} \right) = 0\\
\Rightarrow f\left( x \right) \le 0\forall x\\
\left( 1 \right) \Rightarrow f'\left( x \right) > 0\\
\Rightarrow \left[ \begin{array}{l}
x < - 2\\
1 < x < 2
\end{array} \right.\\
\Rightarrow A
\end{array}$
