Hi.
My question is about removable discontinuities. As an example, consider the function f(x) = (x^2-1)/(x+1), which has a discontinuity at x=-1. This discontinuity can be removed in at least two ways:
1. Define a new function f'(x) = -2, for x=-1, and x^2-1)/(x+1), otherwise.
2. Define a new function f''(x) = x-1 (because x^2-1 = (x+1)(x-1)).
In a sense, the second way is more "elegant", because it is not necessary to define various domains.
Now my problem is the following. Given the function f(x) = (4/x-2)/(x-2), which has a discontinutiy at x=2, how is it possible to remove this discontinuity in the second, more elegant way? (the first way is of course trivial) Is this possible at all?
Many thanks in advance.
My question is about removable discontinuities. As an example, consider the function f(x) = (x^2-1)/(x+1), which has a discontinuity at x=-1. This discontinuity can be removed in at least two ways:
1. Define a new function f'(x) = -2, for x=-1, and x^2-1)/(x+1), otherwise.
2. Define a new function f''(x) = x-1 (because x^2-1 = (x+1)(x-1)).
In a sense, the second way is more "elegant", because it is not necessary to define various domains.
Now my problem is the following. Given the function f(x) = (4/x-2)/(x-2), which has a discontinutiy at x=2, how is it possible to remove this discontinuity in the second, more elegant way? (the first way is of course trivial) Is this possible at all?
Many thanks in advance.