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The problem asks to express the given function \( h(x) = (7x - 2)^8 \) as a composition of two functions \( f \) and \( g \), where \( h(x) = (f \circ g)(x) = f(g(x)) \), and one of the functions is \( 7x - 2 \).

To solve this:

1. We are told that one of the functions should be \( g(x) = 7x - 2 \). Thus, \( g(x) = 7x - 2 \).
2. Next, we need to define \( f(x) \) such that \( f(g(x)) = h(x) \). Notice that \( h(x) \) is \( (7x - 2)^8 \), and \( g(x) = 7x - 2 \), so \( h(x) \) is \( f(g(x)) = f(7x - 2) \).
3. Therefore, \( f(x) \) should take an input and raise it to the 8th power. This means \( f(x) = x^8 \).

Thus, the composition is:
- \( g(x) = 7x - 2 \)
- \( f(x) = x^8 \)

So, \( h(x) = (f \circ g)(x) = f(g(x)) = (7x - 2)^8 \).

Would you like further details or clarification on any part of this solution? Here are some related questions:

1. How do you determine the inner and outer functions in a composition?
2. Can you generalize this method for other functions that are powers of linear expressions?
3. What are some common applications of function composition in real-world scenarios?
4. How do you differentiate a composition of functions using the chain rule?
5. 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.

Express the given function h(x) as a composition of two functions f and g so that h(x) = (f ∘ g)(x), where one of the functions is 7x - 2.

Learn how to express the function h(x) = (7x - 2)^8 as a composition of two functions f and g, where g(x) = 7x - 2 and f(x) = x^8. This solution covers function composition and exponentiation, suitable for high school students.

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