Explain in your own words why the values of X = 5/2 and X = -2 are so important in this equation with respect to the Domain?

Answer 1

In the given equation, there is a denominator (2-x) which cannot be zero. Therefore, X=2 is not in the domain of the function because the denominator will become zero, which is undefined. The two values of X, X=5/2 and X=-2, are important because they are the points where the denominator becomes zero. These points are known as the critical points or singularities of the function. The values of X=5/2 and X=-2 divide the domain into three intervals. The interval (-∞, -2), (-2, 5/2), and (5/2, ∞) make up the domain of the function. The behavior of the function on each of these intervals is different, and therefore these critical points are extremely important in the domain of the function.