Precalculus Examples

Find the Domain y=sec(2x)
Step 1
Set the argument in equal to to find where the expression is undefined.
, for any integer
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 2.3.1.2
Multiply .
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Step 2.3.1.2.1
Multiply by .
Step 2.3.1.2.2
Multiply by .
Step 3
The domain is all values of that make the expression defined.
Set-Builder Notation:
, for any integer
Step 4