To find the domain of the function \( g(x) = \frac{1}{x + 5} \), we need to determine the values of \( x \) for which the function is defined.

The function \( g(x) \) is a rational function, and rational functions are undefined where the denominator is zero. In this case, the denominator is \( x + 5 \). So, we need to find the values of \( x \) that make the denominator zero:

\[
x + 5 = 0
\]

Solving for \( x \), we get:

\[
x = -5
\]

This means that the function \( g(x) = \frac{1}{x + 5} \) is undefined at \( x = -5 \). Therefore, the domain of \( g(x) \) is all real numbers except \( x = -5 \).

**Domain of \( g(x) \):**

\[
\boxed{(-\infty, -5) \cup (-5, \infty)}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. What is the domain of \( f(x) = \frac{2x + 1}{x^2 - 4} \)?
2. How do you find the domain of a square root function, such as \( h(x) = \sqrt{x - 3} \)?
3. What are the steps to determine the range of a rational function like \( g(x) = \frac{1}{x+5} \)?
4. How does the presence of an absolute value in the denominator, such as \( k(x) = \frac{1}{|x| + 2} \), affect the domain?
5. What happens to the domain if we modify \( g(x) = \frac{1}{x + 5} \) to include an additional term, such as \( g(x) = \frac{1}{x + 5} + 2 \)?

**Tip:** For rational functions, always check where the denominator is zero to determine the domain.

Discover how to find the domain of the function g(x) = 1/(x + 5) with detailed steps and explanations. This problem involves understanding rational functions and determining where they are undefined. Suitable for high school students.

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