Mathematics

Problem

A function

g

is defined on all real numbers except at

x = 2

, where its formula would yield

g(x)=\frac{x^2-4}{x-2}

. (a) For

x \neq 2

the expression simplifies to

x+2

. At

x = 2

, no value is currently assigned. a. Part 1: Identify the type of discontinuity that occurs at

x = 2

for

g

and provide a detailed explanation based on the behavior of the limit of

g(x)

x

approaches

2

. b. Part 2: Describe precisely how defining

g

x = 2

could remove this discontinuity and justify, using the definition of continuity, that the newly defined function is continuous at

x = 2