function identity: does $\frac{x^2-4}{x-2} = x+2$ Can you tell me how to resolve the (apparent) paradox that the function:
$$f(x) = \frac{x^2-4}{x-2}$$
is identical to the function:
$$g(x) = x+2$$
because by factoring the numerator:
$$f(x) = \frac{(x+2)(x-2)}{x-2} = x+2$$
But $f(x)$ can't be identical to $g(x)$ since the former is undefined at $x = 2$ and the latter is not ?
Thanks,
Mike

By defintion two functions are said to be identical if they have the same domain  and the same image so $f\neq g$ but we may say that $f$ is extended at $2$ by continuity on the function $g$.
