The inverse of the function $$ h(x) = \frac{1}{x - 9} $$ is ...

Question Analysis
This problem assesses the ability to find the inverse of a rational function.

Key Concept Explanation
To find the inverse, we need to solve for in terms of and then interchange and .

Step-by-step Solution
1. Let , so .
2. Take the reciprocal of both sides: .
3. Solve for :