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

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Answer 1 · 2016-06-30T13:12:30

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

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

$4 - 9 x \neq 0$ $4-9x!=0$

that's

$x \neq \frac{4}{9}$ $x!=4/9$

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

let

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

$4 y - 9 x y = 5 and x \neq \frac{4}{9}$ $4y-9xy=5 and x!=4/9$

$9 x y = 4 y - 5$ $9xy=4y-5$

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

so the range of y is the domain:

$y \neq 0$ $y!=0$

How do you find the domain and range of 54−9x5/(4-9x)?