(3) Write the domain of the following functions:
(1) $f(x)=\frac{1}{|x+3|-1}$ : $\qquad$ ;
(2) $f(x)=\frac{1}{1+\frac{1}{x}}: \square$;
(3) $f(x)=\frac{1}{\sqrt{2 x^{2}+3}}$ : $\qquad$
(4) $f(x)=\frac{\sqrt{x^{2}-4 x+3}}{x^{2}-5 x+6}$ : $\qquad$ ;
(5) $f(x)=\frac{\sqrt{x^{2}-9}}{|x|-5}$ : $\qquad$ ;
(6) $f(x)=\sqrt{2 x-1}+\sqrt{3-4 x}$ :
(3) (1) $\{x \mid x \neq -2$ and $x \neq -4, x \in \mathbf{R}\}$
(2) $\{x \mid x \neq 0$

and $x \neq -1, x \in \mathbf{R}\}$
(3) $\mathbf{R}$
(4) $\{x \mid x \leqslant 1$ or $x > 3\}$
(5) $\{x \mid x \leqslant -3$ or $x \geqslant$
3 and $x \neq \pm 5\}$
(6) $\left\{x \left\lvert\, \frac{1}{2} \leqslant x \leqslant \frac{3}{4}\right.\right\}$