Math Problem Statement
Solution
The functions given are:
The problem asks to find , which is the composition of with itself, meaning .
Step-by-step solution:
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Start by computing :
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Now, substitute into itself:
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Use the expression of , so we substitute into this formula:
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Expand :
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Now substitute this back:
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Simplify:
Thus, .
Would you like any further details or have questions? Here are some related questions for deeper understanding:
- How would you compute ?
- What happens if you reverse the composition to find ?
- Can you explore the domain and range of and ?
- What is the behavior of for large values of ?
- How can you find the inverse of or if they exist?
Tip: When dealing with function composition, always substitute the inner function into the outer function carefully, keeping track of all terms!
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Math Problem Analysis
Mathematical Concepts
Algebra
Function Composition
Polynomial Functions
Formulas
(h ∘ h)(u) = h(h(u))
(u^2 - 3)^2 = u^4 - 6u^2 + 9
Theorems
Function Composition
Suitable Grade Level
Grades 10-12
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