Precalculus Examples

Find the Domain of the Quotient of the Two Functions
Step 1
Find the quotient of the functions.
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Step 1.1
Replace the function designators with the actual functions in .
Step 1.2
Factor using the perfect square rule.
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Step 1.2.1
Rewrite as .
Step 1.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 1.2.3
Rewrite the polynomial.
Step 1.2.4
Factor using the perfect square trinomial rule , where and .
Step 2
Set the denominator in equal to to find where the expression is undefined.
Step 3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 4
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