Bài tập 2.65 trang 133 SBT Toán 12

a) \({4^x} - 2 > 0 \Leftrightarrow {4^x} > 2 \Leftrightarrow x > \frac{1}{2}\)

TXĐ: \(D = \left( {\frac{1}{2}; + \infty } \right)\)

b) \({ \Leftrightarrow \frac{{ - 2}}{3} < x < 1}\)

TXĐ: \({D = \left( {\frac{{ - 2}}{3};1} \right)}\)

c)

\(\begin{array}{l}
\left\{ \begin{array}{l}
\log x + \log \left( {x + 2} \right) \ge 0\\
x > 0\\
x + 2 > 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
\log \left[ {x\left( {x + 2} \right)} \right] \ge 0\\
x > 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
x\left( {x + 2} \right) \ge 1\\
x > 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
{x^2} + 2x - 1 \ge 0\\
x > 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x <  - 1 - \sqrt 2 \\
x >  - 1 + \sqrt 2 
\end{array} \right.\\
x > 0
\end{array} \right. \Leftrightarrow x >  - 1 + \sqrt 2 
\end{array}\)

TXĐ: \(D = \left( { - 1 + \sqrt 2 ; + \infty } \right)\)

d)

\(\begin{array}{l}
\left\{ \begin{array}{l}
\log \left( {x - 1} \right) + \log \left( {x + 1} \right) \ge 0\\
x - 1 > 0\\
x + 1 > 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
\left( {x - 1} \right)\left( {x + 1} \right) \ge 1\\
x > 1
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
{x^2} - 2 \ge 0\\
x > 1
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x \le  - \sqrt 2 \\
x \ge \sqrt 2 
\end{array} \right.\\
x > 1
\end{array} \right. \Leftrightarrow x \ge \sqrt 2 
\end{array}\)

-- Mod Toán 12 HỌC247