# How do you find the domain of the function F(x)= -4/(3x^2-5x-2)?

May 10, 2018

$\left(- \infty , - \frac{1}{3}\right) \cup \left(- \frac{1}{3} , 2\right) \cup \left(2 , \infty\right)$

#### Explanation:

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.

$\text{solve } 3 {x}^{2} - 5 x - 2 = 0 \Rightarrow \left(3 x + 1\right) \left(x - 2\right) = 0$

$3 x + 1 = 0 \Rightarrow x = - \frac{1}{3} \leftarrow \textcolor{red}{\text{excluded value}}$

$x - 2 = 0 \Rightarrow x = 2 \leftarrow \textcolor{red}{\text{excluded value}}$

$\text{domain } x \in \left(- \infty , - \frac{1}{3}\right) \cup \left(- \frac{1}{3} , 2\right) \cup \left(2 , \infty\right)$
graph{-4/(3x^2-5x-2) [-10, 10, -5, 5]}