Find the Domain f(x)=sec(2x)

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Trigonometry

$f (x) = \sec (2 x)$

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

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

Divide each term by $2$ and simplify.

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Divide each term in $2 x = \frac{π}{2} + π n$ by $2$ .

$\frac{2 x}{2} = \frac{π}{2} \cdot \frac{1}{2} + \frac{π n}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} = \frac{π}{2} \cdot \frac{1}{2} + \frac{π n}{2}$

Divide $x$ by $1$ .

$x = \frac{π}{2} \cdot \frac{1}{2} + \frac{π n}{2}$

Multiply $\frac{π}{2} \cdot \frac{1}{2}$ .

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Multiply $\frac{π}{2}$ and $\frac{1}{2}$ .

$x = \frac{π}{2 \cdot 2} + \frac{π n}{2}$

Multiply $2$ by $2$ .

$x = \frac{π}{4} + \frac{π n}{2}$

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

Set-Builder Notation:

${x | x \neq \frac{π}{4} + \frac{π n}{2}}$ , for any integer $n$

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