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

Question

1390 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-30T13:12:30

The domain is made of all real numbers except $4/9$
The range is made of all numbers except 0

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

$4-9x!=0$

that's

$x!=4/9$

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

let

$y=f(x)=5/(4-9x)$

$4y-9xy=5 and x!=4/9$

$9xy=4y-5$

$x=(4y-5)/(9y)$

so the range of y is the domain:

$y!=0$

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