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The problem in the image asks to find functions \( f(x) \) and \( g(x) \) such that \( h(x) = (f \circ g)(x) \), where \( h(x) = |9x^2 - 4| \). 

This means we need to find two functions \( f(x) \) and \( g(x) \) such that:

\[
h(x) = f(g(x))
\]

Given \( h(x) = |9x^2 - 4| \), a reasonable approach is to identify \( g(x) \) as the inner function and \( f(x) \) as the outer function that processes the result of \( g(x) \).

### Step-by-Step Solution:

1. **Outer function \( f(x) \):**
   Since the outer operation is taking the absolute value, a natural choice for \( f(x) \) is:

   \[
   f(x) = |x|
   \]

2. **Inner function \( g(x) \):**
   Now, we need \( g(x) \) such that when we apply \( f(g(x)) \), we recover \( h(x) = |9x^2 - 4| \). The expression inside the absolute value is \( 9x^2 - 4 \), so:

   \[
   g(x) = 9x^2 - 4
   \]

### Final Answer:
\[
f(x) = |x| \quad \text{and} \quad g(x) = 9x^2 - 4
\]

When you compose these functions, you get:
\[
(f \circ g)(x) = f(g(x)) = f(9x^2 - 4) = |9x^2 - 4|
\]
which matches the given \( h(x) \).

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

Here are 5 related questions to deepen understanding:
1. How do you determine the composition of functions in general?
2. Why is the absolute value function appropriate for the outer function \( f(x) \)?
3. Can you think of alternative forms for \( g(x) \) that would still satisfy \( h(x) \)?
4. How would the solution change if \( h(x) \) didn't involve an absolute value?
5. What role does the quadratic structure of \( g(x) \) play in the function composition?

**Tip:** When breaking down a function composition problem, start by identifying key operations (like absolute values or squares) and consider them as candidates for the outer function.

Find f(x) and g(x) such that h(x) = (f ∘ g)(x), where h(x) = |9x^2 - 4|.

This problem asks you to find functions f(x) and g(x) such that h(x) = (f ∘ g)(x), where h(x) = |9x^2 - 4|. This solution uses key algebraic concepts, including function composition and absolute values, suitable for high school students in grades 10-12.

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