Question

Topic : Continuous Extensions.

Assume g(x) is a piecewise function which is:


g(x) = x when x is not equal to 2
g(x) = 1 when x = 2

g(x) is discontinuous.

An extension could be this.


G(x) = x when x is not equal to 2
G(x) = 2 when x is equal to 2


Here's the question:


Could we make a such extension?

G(x) = x/2 when x is not euqal to 2
G(x) = 1 when x = 2