It looks like the image contains a math problem asking for the domain of the functions in interval notation. Let's go through each part to determine the domain.

(a) $f(x) = \frac{x-3}{x-4}$

For this function, the domain is all real numbers except where the denominator equals zero. Set $x - 4 = 0$, which gives $x = 4$. Therefore, the domain is all real numbers except $x = 4$. In interval notation, this is:

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

Would you like help with parts (b) and (c)? Let me know if you need further explanation or details!

Here are some follow-up questions for deeper understanding:

1. Why is the domain of $f(x)$ restricted to $x = 4$?
2. What happens to the function as $x$ approaches 4?
3. How would you find the domain of a rational function in general?
4. How can you check the domain of a function using a graph?
5. What does the concept of a "discontinuity" mean in relation to the domain?

Tip: Always check for values that make the denominator zero when determining the domain of a rational function.