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We are given that \( h(x) = (f \circ g)(x) = (x - 9)^3 \), and we also know that \( g(x) = x - 9 \). We are asked to find \( f(x) \).

### Step-by-step solution:

1. The notation \( (f \circ g)(x) \) means that we are composing two functions, \( f \) and \( g \), such that:
   \[
   h(x) = f(g(x)).
   \]
2. We know that \( g(x) = x - 9 \). So,
   \[
   h(x) = f(g(x)) = f(x - 9).
   \]
3. From the problem, \( h(x) = (x - 9)^3 \). Thus, we have:
   \[
   f(x - 9) = (x - 9)^3.
   \]
4. To find \( f(x) \), notice that the expression \( f(x - 9) = (x - 9)^3 \) suggests that:
   \[
   f(u) = u^3,
   \]
   where \( u = x - 9 \).

Thus, the function \( f(x) \) is:
\[
f(x) = x^3.
\]

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

### Related Questions:
1. How would the solution change if \( g(x) \) were different, for example, \( g(x) = x + 2 \)?
2. How do you find the composition of two functions in general?
3. What is the inverse of the function \( f(x) = x^3 \)?
4. How does the chain rule apply when dealing with compositions of functions like \( f \circ g \)?
5. What if \( h(x) = (x - 9)^n \) where \( n \) is some other exponent?

**Tip:** When working with compositions of functions, always break down the problem step by step, starting with substituting the inner function into the outer function.

Let h(x) = (f ∘ g)(x) = (x - 9)^3. Find f(x) given g(x) = x - 9.

This problem involves finding the function f(x) using function composition, given h(x) = (x - 9)^3 and g(x) = x - 9. Learn step-by-step how to solve for f(x) and understand the relationship between composite functions.

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