To find the domain of the function $f(x) = \frac{x + 2}{5 - x}$, we need to determine where the function is defined.

For rational functions like this one, the function is undefined where the denominator is zero. So, we need to find where $5 - x = 0$.

1. Set the denominator equal to zero: $5 - x = 0$

2. Solve for $x$: $x = 5$

Thus, the function is undefined at $x = 5$. Therefore, the domain of $f(x)$ is all real numbers except $x = 5$.

Final answer: The domain of the function is $(-\infty, 5) \cup (5, \infty)$.

Would you like further details, or do you have any questions? Here are 5 related questions for practice:

1. What is the domain of $f(x) = \frac{1}{x-3}$?
2. How do you find the domain of $f(x) = \frac{2x + 1}{x^2 - 4}$?
3. What happens to a function if its denominator is zero at a certain point?
4. Can you explain the concept of undefined points in rational functions?
5. What would the domain be for $f(x) = \frac{x + 1}{x^2 + x - 6}$?

Tip: Always check the denominator for zeros when finding the domain of a rational function!