Find the domain of the function.
​g(x)equalsStartFraction x plus 7 Over x squared minus 1 EndFraction

To find the domain of the function \( g(x) = \frac{x + 7}{x^2 - 1} \), we need to determine the values of \( x \) for which the function is defined. The function \( g(x) \) will be undefined wherever the denominator is equal to zero.

The denominator of \( g(x) \) is \( x^2 - 1 \). We need to find the values of \( x \) that make the denominator zero:

\[ x^2 - 1 = 0 \]

Solving for \( x \):

\[ x^2 = 1 \]

\[ x = \pm 1 \]

So, the function \( g(x) \) is undefined at \( x = 1 \) and \( x = -1 \).

Thus, the domain of \( g(x) \) is all real numbers except \( x = 1 \) and \( x = -1 \). In interval notation, the domain is:

\[ (-\infty, -1) \cup (-1, 1) \cup (1, \infty) \]

Would you like more details or have any questions?

Here are some questions you might want to ask next:
1. How do you find the domain of a more complex function?
2. Can you explain how to find the range of a function?
3. What is the difference between a function's domain and its range?
4. How do you determine if a function is continuous?
5. Can you provide an example of finding the domain of a function with a square root?

**Tip:** When determining the domain of a function, always check for values that make the denominator zero or result in taking the square root of a negative number.

Discover how to determine the domain of the function g(x) = (x + 7) / (x^2 - 1). This problem involves rational functions and quadratic equations. Suitable for high school students.

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