The function $h(x) = \frac{1}{x-8}$ can be expressed in the form $f(g(x))$ where $g(x) = x - 8$.

To express $h(x)$ in the form $f(g(x))$, let's follow these steps:

1. We are given $g(x) = x - 8$.
2. Then, substituting $g(x)$ into $h(x)$, we have $h(x) = \frac{1}{g(x)}$.

Thus, we can express $h(x)$ as: $h(x) = f(g(x))$ where $f(x) = \frac{1}{x}$.

So, the function $f(x)$ is defined as: $f(x) = \frac{1}{x}$

Would you like further details or have any questions?

Here are 5 related questions:

1. How can you verify that $h(x) = f(g(x))$ for the given functions?
2. What is the domain of the function $h(x) = \frac{1}{x-8}$?
3. How does the transformation $g(x) = x - 8$ affect the graph of $f(x)$?
4. Can you express $h(x)$ in the form $f(g(x))$ with a different function $f(x)$?
5. How would the function $h(x)$ change if $g(x) = x + 8$?

Tip: When working with composite functions, always substitute the inner function into the outer function to check if they match the given function.