Finite Math Examples

Find the Domain of the Product of the Functions C(x)=27000+55x+0.2x^2 , R(x)=445x-0.8x^2
,
Step 1
Find the product of the functions.
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Step 1.1
Replace the function designators with the actual functions in .
Step 1.2
Simplify.
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Step 1.2.1
Expand by multiplying each term in the first expression by each term in the second expression.
Step 1.2.2
Simplify terms.
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Step 1.2.2.1
Simplify each term.
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Step 1.2.2.1.1
Multiply by .
Step 1.2.2.1.2
Multiply by .
Step 1.2.2.1.3
Rewrite using the commutative property of multiplication.
Step 1.2.2.1.4
Multiply by by adding the exponents.
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Step 1.2.2.1.4.1
Move .
Step 1.2.2.1.4.2
Multiply by .
Step 1.2.2.1.5
Multiply by .
Step 1.2.2.1.6
Rewrite using the commutative property of multiplication.
Step 1.2.2.1.7
Multiply by by adding the exponents.
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Step 1.2.2.1.7.1
Move .
Step 1.2.2.1.7.2
Multiply by .
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Step 1.2.2.1.7.2.1
Raise to the power of .
Step 1.2.2.1.7.2.2
Use the power rule to combine exponents.
Step 1.2.2.1.7.3
Add and .
Step 1.2.2.1.8
Multiply by .
Step 1.2.2.1.9
Rewrite using the commutative property of multiplication.
Step 1.2.2.1.10
Multiply by by adding the exponents.
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Step 1.2.2.1.10.1
Move .
Step 1.2.2.1.10.2
Multiply by .
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Step 1.2.2.1.10.2.1
Raise to the power of .
Step 1.2.2.1.10.2.2
Use the power rule to combine exponents.
Step 1.2.2.1.10.3
Add and .
Step 1.2.2.1.11
Multiply by .
Step 1.2.2.1.12
Rewrite using the commutative property of multiplication.
Step 1.2.2.1.13
Multiply by by adding the exponents.
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Step 1.2.2.1.13.1
Move .
Step 1.2.2.1.13.2
Use the power rule to combine exponents.
Step 1.2.2.1.13.3
Add and .
Step 1.2.2.1.14
Multiply by .
Step 1.2.2.2
Simplify by adding terms.
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Step 1.2.2.2.1
Add and .
Step 1.2.2.2.2
Add and .
Step 2
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
Step 3