Question

give an example of a function g(x) that is continuous for all values of x except x=-1 where it has a nonremovable discontinuity. Explain how you know that g is discontinuous there and why the discontinuity is not removable

Answer 1

it isn't removable because... well because it isn't
it is a jump

Answer 2

whats the equation?

Answer 3

it is a piecewise function, make up your own
or you could use something like
\[f(x)=\frac{1}{x+1}\] which has a vertical asymptote at \(x=-1\) but is continuous everywhere else