Question #N133
The function *f* is defined by $f(x) = \frac{x^2 - 4}{x-2}$. For what value of *x* does the function *f* have a removable discontinuity?
A. -4
B. -2
C. 2
D. 4
Correct Answer is: C
A removable discontinuity occurs at a point where the function is undefined due to a zero in the denominator, but the limit of the function exists at that point. In this case, the function is undefined when *x* = 2 because it results in a zero in the denominator. However, the function can be simplified by factoring the numerator: $f(x) = \frac{x^2 - 4}{x-2} = \frac{(x+2)(x-2)}{x-2} = x+2$ for all *x* not equal to 2. Therefore, the limit of *f* as *x* approaches 2 exists and is equal to 4. Since the limit exists, the function has a removable discontinuity at *x* = 2.