How to Find the Domain of a Function

What to look for

$x - 3 \neq = 0$

The domain is all real numbers except $x = 3$ .

$x - 2 \geq 0$

The domain is $x \geq 2$ .

$x + 5 > 0$

The domain is $x > - 5$ .

The root needs $x \geq 0$ , and the denominator needs $x \neq = 4$ .

The domain is $x \geq 0$ with $x \neq = 4$ .

$\frac{x ^{2} - 4}{x - 2} = x + 2$ , so the domain is all real numbers.

Find the domain before you simplify. The original function is undefined at $x = 2$ , even though the simplified version isn't.

$f (x) = \frac{1}{x ^{2} - 9}$
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All real numbers except $x = 3$ and $x = - 3$
$f (x) = 6 - 2 x$
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$x \leq 3$
$f (x) = ln (2 x - 4)$
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$x > 2$

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