Math Problem Statement
What is (fg)(x)? f(x)= – 3x2–2x+1 g(x)=2x+4 Write your answer as a polynomial or a rational function in simplest form.
Solution
To find , we need to multiply the functions and . This is denoted as:
Given the functions: and
We will multiply them:
To simplify, we distribute each term of by each term of :
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Multiply by each term in :
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Multiply by each term in :
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Multiply by each term in :
Now, combine all the terms:
Combine like terms:
So, the simplified form of is:
Would you like more details on any step or have further questions?
Here are 5 related questions:
- How do you factor polynomials such as ?
- What are the steps for finding the product of two polynomials in general?
- How do you check if a function is a factor of another polynomial?
- What is the meaning of the composition of functions ?
- How can you apply this to rational functions?
Tip: When multiplying polynomials, always distribute each term carefully and remember to combine like terms at the end for simplicity!
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Math Problem Analysis
Mathematical Concepts
Function Multiplication
Polynomial Multiplication
Algebra
Formulas
(fg)(x) = f(x) * g(x)
Theorems
Distributive Property
Suitable Grade Level
Grades 9-12
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