Question

Give an example of a function with both a removable and a non-removable discontinuity.

Answer 1

A removable discontinuity is often of the form (x-a)/(x-a). Non-removable discontinuities often happen due to a zero in the denominator. So if we build both of these things into our function, we might get something like\[f(x)=\frac{(x-a)}{(x-a)(x-b)}\]The discontinuity at x=a is removable; the discontinuity at x=b is not.