To find the domain of the function $f(x) = \frac{2}{x-4}$, we need to identify any values of $x$ that would cause the denominator to be zero. The function will be undefined when the denominator is zero, as division by zero is not allowed.

Step 1: Set the denominator equal to zero and solve for $x$:

$x - 4 = 0$

$x = 4$

So, the function is undefined at $x = 4$.

Step 2: Write the domain

The domain consists of all real numbers except $x = 4$. In interval notation, the domain is:

$(-\infty, 4) \cup (4, \infty)$

Thus, the domain of $f(x) = \frac{2}{x-4}$ is all real numbers except $x = 4$.

Would you like a more detailed explanation or have any specific questions?

Related questions:

1. What is the range of the function $f(x) = \frac{2}{x-4}$?
2. How does the graph of $f(x) = \frac{2}{x-4}$ behave near $x = 4$?
3. How would the domain change if the function were $f(x) = \frac{2}{x+4}$?
4. How can we find vertical asymptotes for rational functions like this?
5. How do we identify if a function is continuous or discontinuous?

Tip: Always check for values of $x$ that make the denominator zero to find restrictions in the domain.