We are asked to express the function $h(x) = \frac{1}{x - 5}$ in the form $f \circ g$, where $g(x) = x - 5$, and we need to find the function $f(x)$.

In functional notation, $f \circ g$ means $f(g(x))$.

Given: $h(x) = \frac{1}{x - 5}$ and $g(x) = x - 5,$ we can rewrite $h(x)$ as: $h(x) = f(g(x)) = f(x - 5).$

Since $h(x) = \frac{1}{x - 5}$, we compare it to $f(x - 5)$, which implies that: $f(x) = \frac{1}{x}.$

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

Would you like further explanation, or do you have any additional questions?

Here are 5 related questions to expand your understanding:

1. How do we determine $g(x)$ when decomposing a function in the form $f \circ g$?
2. Can you decompose other functions like $h(x) = \frac{1}{x+2}$ in a similar way?
3. What is the general process to express any given function as a composition of two functions?
4. How would $f$ and $g$ change if $h(x) = \frac{2}{x-3}$?
5. What are the properties of compositions of functions, and how do they affect the final expression?

Tip: When decomposing a function, always start by identifying the inner function $g(x)$, which is applied first, and then identify the outer function $f(x)$, which is applied to the result of $g(x)$.