Question

Does the discontinuity appear to be removable or essential? f(x)=(x^(2)-4)/(x-2);a=2

Answer 1

The discontinuity at x = 2 in the given function f(x) = (x^2-4)/(x-2) is removable.

Step-by-step explanation:

The given function is f(x) = (x2-4)/(x-2), and we need to determine whether the discontinuity at x = 2 is removable or essential.

To check if the discontinuity is removable, we need to see if the function can be redefined in such a way that the limit exists at x = 2.

Let's simplify the function: f(x) = (x+2)(x-2)/(x-2).

Now, we can cancel out the factors of (x-2) in the numerator and denominator, resulting in f(x) = x+2.

Since f(x) = x+2 is defined and continuous at x = 2, we can conclude that the discontinuity at x = 2 is removable.