# How do you find the domain and range of g(x)=6/(3-5x)?

Jan 17, 2017

The domain is ${D}_{g} \left(x\right) = \mathbb{R} - \left\{\frac{3}{5}\right\}$
The range is ${R}_{g} \left(x\right) = \mathbb{R} - \left\{0\right\}$

#### Explanation:

$g \left(x\right) = \frac{6}{3 - 5 x}$

As we cannot divide by $0 ,$, $x \ne \frac{3}{5}$

The domain of $g \left(x\right)$ is ${D}_{g} \left(x\right) = \mathbb{R} - \left\{\frac{3}{5}\right\}$

${\lim}_{x \to - \infty} g \left(x\right) = {\lim}_{x \to - \infty} \frac{6}{- 5 x} = {0}^{+}$

${\lim}_{x \to + \infty} g \left(x\right) = {\lim}_{x \to + \infty} \frac{6}{- 5 x} = {0}^{-}$

The range of $f \left(x\right)$ is ${R}_{g} \left(x\right) = \mathbb{R} - \left\{0\right\}$