Math Problem Statement
Solution
The problem asks to express the given function as a composition of two functions and , where , and one of the functions is .
To solve this:
- We are told that one of the functions should be . Thus, .
- Next, we need to define such that . Notice that is , and , so is .
- Therefore, should take an input and raise it to the 8th power. This means .
Thus, the composition is:
So, .
Would you like further details or clarification on any part of this solution? Here are some related questions:
- How do you determine the inner and outer functions in a composition?
- Can you generalize this method for other functions that are powers of linear expressions?
- What are some common applications of function composition in real-world scenarios?
- How do you differentiate a composition of functions using the chain rule?
- What happens if the inner function is more complex than a linear expression?
Tip: When composing functions, always try to identify which part of the original function can be isolated and treated as the "inner" function.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Exponents
Algebra
Formulas
h(x) = (f ∘ g)(x) = f(g(x))
g(x) = 7x - 2
f(x) = x^8
Theorems
Composition of Functions
Suitable Grade Level
Grades 9-12
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