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.