Math Problem Statement
Solution
The question asks to find , which means . Given the functions:
We need to compute , which involves substituting into .
Step-by-step Solution:
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Start by substituting into :
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Now, substitute wherever there is in :
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Expand : So,
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Expand the terms:
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Combine like terms:
Thus, .
The correct answer is option E: .
Would you like more details on any part of this process? Here are five related questions to deepen your understanding:
- How is the composition of functions defined?
- What is the general method to simplify ?
- How can the distributive property help in expanding expressions like ?
- Can the process of function composition be reversed? How would differ here?
- How would you approach the same problem if had a cubic term?
Tip: When composing functions, always make sure to substitute the entire expression for correctly into .
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Math Problem Analysis
Mathematical Concepts
Function Composition
Polynomials
Algebra
Formulas
g(f(x)) = g(x+2)
(x+a)^2 = x^2 + 2ax + a^2
Theorems
Function Composition Theorem
Distributive Property
Suitable Grade Level
Grades 10-12
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