The domain of the function $f ( x ) = \frac { 3 } { 2 x ^ { 2 } - 5 x - 3 }$ is

A) $\left( - \frac { 1 } { 2 } , 3 \right)$
B) $\left( - \infty , - \frac { 1 } { 2 } \right) \cup ( 3 , \infty )$
C) $( - \infty , - 3 ) \cup \left( - 3 , \frac { 1 } { 2 } \right)$
D) $( - \infty , - 3 ) \cup \left( - 3 , \frac { 1 } { 2 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$
E) $\left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( - \frac { 1 } { 2 } , 3 \right) \cup ( 3 , \infty )$

Question

The domain of the function $f ( x ) = \frac { 3 } { 2 x ^ { 2 } - 5 x - 3 }$ is

A) $\left( - \frac { 1 } { 2 } , 3 \right)$
B) $\left( - \infty , - \frac { 1 } { 2 } \right) \cup ( 3 , \infty )$
C) $( - \infty , - 3 ) \cup \left( - 3 , \frac { 1 } { 2 } \right)$
D) $( - \infty , - 3 ) \cup \left( - 3 , \frac { 1 } { 2 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$
E) $\left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( - \frac { 1 } { 2 } , 3 \right) \cup ( 3 , \infty )$

Quizplus · Accepted Answer

The domain of the function is all real numbers except where the denominator is zero. Solving $2x^2 - 5x - 3 = 0$ gives the roots $x = -\frac{1}{2}$ and $x = 3$. Thus, the domain is $\left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( - \frac { 1 } { 2 } , 3 \right) \cup ( 3 , \infty )$.

The Domain of the Function f(x)=32x2−5x−3f ( x ) = \frac { 3 } { 2 x ^ { 2 } - 5 x - 3 }f(x)=2x2−5x−33​

The Domain of the Function $f ( x ) = \frac { 3 } { 2 x ^ { 2 } - 5 x - 3 }$