# How do you find the domain and range of 5/(4-9x)?

Jun 30, 2016

The domain is made of all real numbers except $\frac{4}{9}$
The range is made of all numbers except 0

#### Explanation:

you can find the domain by excluding x values that make null the denominator:

$4 - 9 x \ne 0$

that's

$x \ne \frac{4}{9}$

Let's find the inverse function through these simple steps:

let

$y = f \left(x\right) = \frac{5}{4 - 9 x}$

$4 y - 9 x y = 5 \mathmr{and} x \ne \frac{4}{9}$

$9 x y = 4 y - 5$

$x = \frac{4 y - 5}{9 y}$

so the range of y is the domain:

$y \ne 0$