We are asked to express the function $h(x) = \frac{1}{x - 2}$ in the form $f \circ g$, where $g(x) = x - 2$, and we need to find the function $f(x)$.

To solve this, we follow these steps:

1. We are given that $g(x) = x - 2$, and we know that $h(x) = f(g(x))$.
2. To express $h(x)$ in terms of $f(x)$, substitute $g(x)$ into $h(x)$: $h(x) = \frac{1}{x - 2} = f(g(x)) = f(x - 2).$
3. This implies that $f(x - 2) = \frac{1}{x - 2}$.
4. Therefore, the function $f(x)$ must be: $f(x) = \frac{1}{x}.$

Thus, the function $f(x)$ is $f(x) = \frac{1}{x}$.

Let me know if you would like further explanation or have any other questions!

Here are some related questions:

1. What is the composition of functions $f \circ g$?
2. How do you find the inverse of a composite function?
3. How does the transformation $g(x) = x - 2$ affect the graph of a function?
4. How do you verify the composition of two functions?
5. Can you express $h(x) = \frac{1}{x+3}$ in the form $f \circ g$?

Tip: When decomposing functions into compositions, it's helpful to identify the inner and outer functions based on transformations applied to the variable.