Question

What are the removable and non-removable discontinuities, if any, of `f(x)=2/(x+1)`?

Answer 1

There is a non-removable discontinuity when `x=-1`.

Explanation:

The only discontinuity you can have with a quotient of continuous functions is when the denominator is `0`.

In your case, when `x+1 = 0 \iff x = -1`.

If you want to know if the discontinuity is removable, you can just compute the limit and see if it exists :

`\lim_( x \rightarrow -1) f(x) = \lim_( x \rightarrow -1) 2/(x+1) = +- oo`.

Therefore, it is not removable.