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

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Answer 1 · 2016-04-02T08:19:07

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

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.

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