Math Problem Statement
Solution
In the image you uploaded, you have the functions and . You are tasked with finding the composition of the functions, denoted as , which means .
Let's calculate :
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Substitute into :
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Replace in with :
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Distribute and simplify:
So, the composition is .
If you have any further questions or need more details on this process, feel free to ask!
Related Questions:
- What is the graphical interpretation of the composition of functions?
- Can you determine using the same functions?
- What happens if the order of composition is reversed?
- How do compositions affect the domain and range of the resulting function?
- Is there a real-life scenario where composition of functions is applied?
Tip:
When solving for a function composition, always substitute the entire function for each instance of in the outer function and then simplify.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Polynomial Operations
Formulas
f(g(x)) = f(h(x)) for g(x) = h(x)
Theorems
Composition of functions
Suitable Grade Level
College
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