# How do you find the domain and range of g(x)=8/(3-7x)?

Nov 20, 2017

The domain is $\mathbb{R} - \left\{\frac{7}{3}\right\}$. The range is $\mathbb{R} - \left\{0\right\}$

#### Explanation:

The denominator must be $\ne 0$

Therefore,

$3 - 7 x \ne 0$

$7 x \ne 3$

$x \ne \frac{3}{7}$

So, the domain is $\mathbb{R} - \left\{\frac{7}{3}\right\}$

Let

$y = \frac{8}{3 - 7 x}$

$y \left(3 - 7 x\right) = 8$

$3 y - 7 x y = 8$

$7 x y = 3 y - 8$

$x = \frac{3 y - 8}{7 y}$

The same reasoning as above

$y \ne 0$

The range is $\mathbb{R} - \left\{0\right\}$

graph{8/(3-7x) [-12.66, 12.65, -6.33, 6.33]}