To find the domain of the function $f(x) = \frac{1}{2x - 10}$, we need to identify the values of $x$ that make the denominator equal to zero, as the function will be undefined at these points.

Step-by-step:

1. Set the denominator equal to zero: $2x - 10 = 0$
2. Solve for $x$: $2x = 10$ $x = 5$

So, the function is undefined at $x = 5$. This means that the domain excludes $x = 5$.

Domain:

In interval notation, the domain is: $(-\infty, 5) \cup (5, \infty)$

Let me know if you'd like more details or explanations. Here are a few follow-up questions to consider:

1. What happens to the function $f(x)$ as $x$ approaches 5 from the left and the right?
2. Can you explain why the function is undefined at $x = 5$?
3. How would the domain change if the function had a different denominator, say $2x - 8$?
4. What is the range of this function given the domain we just found?
5. How do you find the vertical asymptote of a rational function?

Tip: Always check the denominator of a rational function to identify points where the function may be undefined.