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To find the domain of the rational function:

\[
f(x) = \frac{x - 6}{x + 7}
\]

we need to identify any values of \( x \) that would make the function undefined. A rational function is undefined when the denominator equals zero.

1. Set the denominator equal to zero:
   \[
   x + 7 = 0
   \]
   
2. Solve for \( x \):
   \[
   x = -7
   \]

Thus, the function is undefined at \( x = -7 \). The domain of \( f(x) \) includes all real numbers except \( x = -7 \).

In interval notation, the domain is:

\[
(-\infty, -7) \cup (-7, \infty)
\]

Would you like further details or have any questions?

### Related Questions
1. What is the domain of a function if it includes square roots or other radicals?
2. How do you determine the domain of a rational function with multiple factors in the denominator?
3. How does the domain change if there are complex numbers involved?
4. What is the domain of a polynomial function?
5. Can a function have a domain restricted by conditions other than division by zero?

### Tip
Always check the denominator of a rational function for values that make it zero, as these are the values excluded from the domain.

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

Understand how to find the domain of the rational function f(x) = (x - 6) / (x + 7). This solution explains how to identify values that make the denominator zero, showing that the domain excludes x = -7. Ideal for high school students in Grades 10-12.

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