The function given in the image is:

$f(x) = \frac{7}{x+7} + \frac{6}{x-8}$

To find the domain of the function, we need to determine where the function is undefined. The function becomes undefined wherever the denominators of the fractions equal zero.

1. For the first term $\frac{7}{x+7}$, the denominator is zero when: $x + 7 = 0 \implies x = -7$

2. For the second term $\frac{6}{x-8}$, the denominator is zero when: $x - 8 = 0 \implies x = 8$

Thus, the function is undefined at $x = -7$ and $x = 8$.

Therefore, the domain of the function is all real numbers except $x = -7$ and $x = 8$. In interval notation, the domain is:

$(-\infty, -7) \cup (-7, 8) \cup (8, \infty)$

Would you like more details or have any questions about this?

Here are 5 related questions you might find helpful:

1. How do you find the domain of a function with more complex denominators?
2. What happens to the graph of the function at $x = -7$ and $x = 8$?
3. Can the domain of a function change if we simplify it?
4. How do asymptotes relate to the domain of rational functions?
5. How do we find the domain of a function that involves square roots as well?

Tip: Always check for values that make the denominator zero when working with rational functions.