Finite Math Examples

Find the Domain of the Quotient of the Two Functions
,
Step 1
Find the quotient of the functions.
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Replace the function designators with the actual functions in .
Simplify the numerator.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2
Set the denominator in equal to to find where the expression is undefined.
Step 3
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
Step 4
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 5
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