To determine the values of x that are not in the domain of a function g, we first need to understand the function’s defining characteristics. Generally, values that cause division by zero, square roots of negative numbers, or logarithms of non-positive numbers often lead to restrictions in the domain.
For example, suppose g(x) = 1/(x – 2). In this case, we encounter an issue when x equals 2 because it would lead to division by zero. Therefore, x = 2 is a value that is not in the domain of g.
Similarly, if our function were g(x) = √(x – 3), the square root requires that the expression inside the root must be non-negative. Thus, x – 3 ≥ 0 leads us to the conclusion that x < 3 is not part of the domain.
In summary, to find all values of x not in the domain of g, analyze the function for points where it becomes undefined, and consider any constraints associated with the operations within the function.