The domain of $f ( x ) = \frac { 3 x - 2 } { 9 x ^ { 2 } - 4 }$ is

A) $\left( - \infty , - \frac { 2 } { 3 } \right)$
B) $\left( - \infty , \frac { 2 } { 3 } \right)$
C) $\left( - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right)$
D) $\left( - \infty , - \frac { 2 } { 3 } \right) \cup \left( \frac { 2 } { 3 } , \infty \right)$
E) $\left( - \infty , - \frac { 2 } { 3 } \right) \cup \left( - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right) \cup \left( \frac { 2 } { 3 } , \infty \right)$

Question

The domain of $f ( x ) = \frac { 3 x - 2 } { 9 x ^ { 2 } - 4 }$ is

A) $\left( - \infty , - \frac { 2 } { 3 } \right)$
B) $\left( - \infty , \frac { 2 } { 3 } \right)$
C) $\left( - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right)$
D) $\left( - \infty , - \frac { 2 } { 3 } \right) \cup \left( \frac { 2 } { 3 } , \infty \right)$
E) $\left( - \infty , - \frac { 2 } { 3 } \right) \cup \left( - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right) \cup \left( \frac { 2 } { 3 } , \infty \right)$

Quizplus · Accepted Answer

The domain of the function is all real numbers except where the denominator is zero. The denominator $9x^2 - 4$ is zero when $x = \pm \frac{2}{3}$. Thus, the domain excludes these points.

The Domain Of f(x)=3x−29x2−4f ( x ) = \frac { 3 x - 2 } { 9 x ^ { 2 } - 4 }f(x)=9x2−43x−2​

The Domain Of $f ( x ) = \frac { 3 x - 2 } { 9 x ^ { 2 } - 4 }$