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We are given the function:

\[
f(x) = \frac{x^2 + 7x - 18}{x^2 - 1}
\]

We need to find the values of \( x \) that are **NOT** in the domain of \( f(x) \).

The domain of a rational function is all real numbers except where the denominator is zero. To find the excluded values, we need to solve for \( x \) when the denominator is equal to zero:

\[
x^2 - 1 = 0
\]

This simplifies to:

\[
x^2 = 1
\]

Taking the square root of both sides:

\[
x = \pm 1
\]

So, \( x = 1 \) and \( x = -1 \) are the values that make the denominator zero, meaning these values are **NOT** in the domain of the function.

Therefore, the values of \( x \) that are not in the domain are:

\[
x = -1, 1
\]

Would you like a further breakdown, or do you have any questions? Here are 5 related questions to explore further:

1. How would you determine the domain of a more complex rational function?
2. What happens to the graph of a function at points not in the domain?
3. How does factoring help simplify finding restrictions in the domain?
4. What is the difference between holes and vertical asymptotes in rational functions?
5. Can the numerator of a rational function affect its domain?

**Tip:** Always check both the numerator and denominator to see if any common factors can simplify the function before solving for domain restrictions.

Find all values of x that are NOT in the domain of f(x) = (x^2 + 7x - 18) / (x^2 - 1).

Learn how to find the values of x that are not in the domain of a rational function, f(x) = (x^2 + 7x - 18) / (x^2 - 1). This problem explores restrictions in rational functions and factoring techniques, suitable for students in Grades 9-12.

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