ANSWER
[tex]( - \infty , - \frac{4}{3} ) \cup( \frac{1}{2} , \infty )[/tex]
EXPLANATION
The given function is
[tex]f(x) = \sqrt{ \frac{2x - 1}{3x + 4} } [/tex]
The domain refers to all values of x for which f(x) is defined.
This function is defined if
[tex] \frac{2x - 1}{3x + 4} > 0[/tex]
This implies that
[tex]x \: < \: - \frac{4}{3} \: or \: x \: > \: \frac{1}{2} [/tex]
Or
[tex]( - \infty , - \frac{4}{3} ) \cup( \frac{1}{2} , \infty )[/tex]
