The function given in the image is:

$g(x) = \frac{x - 3}{x^2 - 4}$

To determine the values of $x$ that are NOT in the domain of the function, we need to find where the denominator is zero because division by zero is undefined.

The denominator is $x^2 - 4$. We set this equal to zero and solve for $x$:

$x^2 - 4 = 0$ $x^2 = 4$ $x = \pm 2$

So, the values of $x$ that are not in the domain of the function are $x = 2$ and $x = -2$.

Final Answer:

$x = -2, 2$

Let me know if you'd like further details or have any questions!

Related Questions:

1. What is the general definition of the domain of a function?
2. Why can't functions include values that cause division by zero?
3. How do we solve equations involving quadratic expressions like $x^2 - 4 = 0$?
4. Can this function have any other restrictions on its domain besides division by zero?
5. What is the significance of the numerator in this function?

Tip:

Always check the denominator of a rational function first to find where the function is undefined.