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

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

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Answer 1 · 2016-10-03T21:49:35

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

Explanation:

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

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

$x + 9 \neq a 0$ $x+9!=color(white)a0$
$a - 9 a a - 9$ $color(white)(a)-9color(white)(aa)-9$

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

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

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

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

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Explanation:

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