3. TXĐ:
$\left\{ \begin{array}{l}
1 - 4{x^2} \ge 0\\
x \ne 0
\end{array} \right.$
$ \bullet - \frac{1}{2} \le x < 0 \Rightarrow 1 - 4{x^2} < 0$
$ \Rightarrow 1 - \sqrt {1 - 4{x^2}} > 0 \Rightarrow \frac{{1 - \sqrt {1 - 4{x^2}} }}{x} < 0 (1)$ đúng
$\bullet 0 < x \le \frac{1}{3} \Rightarrow 1 - 3x < 0 \Leftrightarrow (1)$ đúng
$\bullet \frac{1}{3} < x \le \frac{1}{2} \Rightarrow 1 - 3x > 0$
$\begin{array}{l}
(1) \Leftrightarrow {(1 - 3x)^2} < 1 - 4{x^2} \Leftrightarrow 13{x^2} - 6x < 0\\
\Leftrightarrow 13x\left( {x - \frac{6}{{13}}} \right) < 0\forall x \in (\frac{1}{3};\frac{1}{2}{\rm{]}}
\end{array}$
Vậy ($1$) đúng $\forall x \in [ - \frac{1}{2};0{\rm{)}}\bigcup$ $(0;\frac{1}{2}{\rm{]}}$