Find all values of x that are not in the domain of g, where g(x) = (x - 7) / (x² - 3x - 10).

Functions can be of many types, which include algebraic, trigonometric, or differential functions. We will solve this problem using algebraic functions.

Answer: The values of x that are not in the domain of g, where g(x) = (x - 7) / (x² - 3x - 10) are x = -2 and x = 5.

Let's understand the solution in detail.

Explanation:

Given function: g(x) = (x - 7) / (x² - 3x - 10)

We know that the denominator of any function can't be zero for it to be defined.

Hence, if (x² - 3x - 10) is equal to zero, then the function g is not defined.

Hence, we solve (x² - 3x - 10) = 0

⇒ (x² - 3x - 10) = 0

⇒ x² - 5x + 2x - 10 = 0

⇒ x(x - 5) + 2(x - 5) = 0

⇒ (x + 2)(x - 5) = 0

Hence, x + 2 = 0 or x - 5 = 0

So, if x = -2 or x = 5, then the value of g will not be defined as the denominator will become zero.

Therefore, the values of x that are not in the domain of g are x = -2 and x = 5.