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.
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 for (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.