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

In your question to determine if a function is both a removable and non removable discontinuity is to get the value of its variable either its graph has hole and also it will jump or its an asymptote in the graph. The best example to this is f (x) = x - 1 (x - 1) (x - 2) f (x) = x-1 (x-1) (x-2)