Let g(x)= x-2 x^ 2 -9

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

g(x)=\frac{\sqrt{x-2}}{x^{2}-9}, \qquad x\in\mathbb R.

(i) Find the set of all real numbers for which

g(x)

is defined. (ii) Identify every point in that set where

g

is not continuous. (iii) Express, in interval notation, the complete set on which

g

is continuous. (iv) Classify the discontinuity at each point found in part (ii) as removable, jump, or infinite, giving a brief reason.