Precalculus Examples

$\tan (\arctan (x))$

Step 1

Set the argument in $\tan (\arctan (x))$ equal to $\frac{π}{2} + π n$ to find where the expression is undefined.

$\arctan (x) = \frac{π}{2} + π n$ , for any integer $n$

Step 2

Take the inverse arctangent of both sides of the equation to extract $x$ from inside the arctangent.

$x = \tan (\frac{π}{2} + π n)$

Step 3

The domain is all values of $x$ that make the expression defined.

Set-Builder Notation:

${x | x \neq \tan (\frac{π}{2} + π n)}$ , for any integer $n$

Step 4