How would you "remove the discontinuity" of f ? In other words, how would you define f(2) in order to make f continuous at 2?

Question

f(x) = (x^2-x-2)/(x-2)

F(2) =

Answer 1

f(x) = (x^2-x-2)/(x-2) = (x-2)(x+1)/(x-2) = x+1

for all x not = 2

F(x) = x+1

for all x, including x=2

f(x) is a straight line with a "hole" in it at the point (2,3)

F(x) is the same straight line with the "hole" filled in