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To find the values of \( x \) that are **not** in the domain of the function \( g(x) \), we need to identify the values that make the denominator equal to zero. The function \( g(x) \) is given by:

\[ g(x) = \frac{x + 5}{x^2 - 3x - 40} \]

We need to find the roots of the denominator \( x^2 - 3x - 40 \). To do this, we solve the equation:

\[ x^2 - 3x - 40 = 0 \]

We can factor this quadratic equation:

\[ x^2 - 3x - 40 = (x - 8)(x + 5) = 0 \]

Setting each factor to zero gives the solutions:

\[ x - 8 = 0 \implies x = 8 \]
\[ x + 5 = 0 \implies x = -5 \]

Therefore, the values of \( x \) that are **not** in the domain of \( g \) are \( x = 8 \) and \( x = -5 \).

Hence, the answer is:

\[ x = 8, -5 \]

Would you like more details or have any questions?

Here are 5 more questions you might want to ask:

1. How do you find the domain of a rational function?
2. What are vertical asymptotes and how do you find them?
3. Can you explain the process of factoring quadratic equations?
4. How do you determine if a function has any holes in its graph?
5. What are the steps to simplify complex rational expressions?

**Tip:** When finding the domain of a function, always check for values that make the denominator zero, as these values will not be included in the domain.

Learn how to identify values not in the domain of the function g(x) = (x + 5) / (x^2 - 3x - 40) by finding roots of the denominator. Includes step-by-step solutions, quadratic equation factoring, and rational function domain determination. Suitable for high school students.

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