How do you find the domain of $y=(2x)/(x+9)$ ?

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Answer 1 · 2016-10-03T21:49:35

$x!=-9$ or interval notation $(-oo,-9) U (-9,oo)$

If a value of $x$ results in $y$ being "undefined", that value of $x$ is not included in the domain. The domain is the allowed values of $x$ .

For a rational equation like this example, dividing by zero will result in an undefined $y$ . So, the denominator should not equal zero.

$x+9!=color(white)a0$
$color(white)(a)-9color(white)(aa)-9$

$x!=-9$

A value of $-9$ will result in a zero in the denominator, so $-9$ is not be included in the domain.

In interval notation, this is written as $(-oo,-9)U(-9,oo)$

How do you find the domain of y=(2x)/(x+9)y=(2x)/(x+9)?