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.