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The question in your image asks to express the given function \( h(x) \) as a composition of two functions \( f \) and \( g \), such that \( h(x) = (f \circ g)(x) = f(g(x)) \).

The given function is:

\[
h(x) = \sqrt[5]{x^7} - 4
\]

### Step 1: Break Down \( h(x) \) into Two Functions
We need to identify two functions \( f(x) \) and \( g(x) \) such that:
\[
h(x) = f(g(x))
\]

Let's first handle the inside part:
- The function under the radical is \( x^7 \). We can choose \( g(x) = x^7 \).

Now, we are left with \( f(x) \), which should operate on \( g(x) \). Since we are applying a fifth root and then subtracting 4, we define:
\[
f(x) = \sqrt[5]{x} - 4
\]

### Step 2: Verify
Now, compose the functions to verify:
\[
h(x) = f(g(x)) = f(x^7) = \sqrt[5]{x^7} - 4
\]
This matches the given \( h(x) \).

### Final Answer
The functions are:
\[
f(x) = \sqrt[5]{x} - 4
\]
\[
g(x) = x^7
\]

Would you like further details on this solution or have any other questions?

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Here are 5 related questions to explore:
1. How do you compose two functions in general?
2. What is the difference between composing and adding functions?
3. How can we reverse a composition of functions?
4. What are some real-life examples of function composition?
5. How does the chain rule apply to compositions of functions in calculus?

**Tip:** When breaking down a function for composition, always start by identifying the innermost operation, which can help define the function \( g(x) \).

Express the given function h(x) as a composition of two functions f and g so that h(x) = (f ∘ g)(x) = f(g(x)), where one of the functions is h(x) = 7√x^5 - 4.

Learn how to express the function h(x) = 7√x^5 - 4 as a composition of two functions. This problem explores key mathematical concepts such as function composition and radical functions. Suitable for students in Grades 10-12.

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