https://file.aiquickdraw.com/mathbot/file/1727924950864ooh6jn6j.jpg

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.

Find the domain of the function f(x) = 7/(x+7) + 6/(x-8)

Learn how to find the domain of the rational function f(x) = 7/(x+7) + 6/(x-8) by identifying where the function is undefined. This example demonstrates key algebraic principles and domain theorem for rational functions. Ideal for students in Grades 9-12.

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