Question

Describe the interval(s)on which the function f(x)=(x-11/x^2-121) is continuous.

Answer 1

f(x) = 1/(x+11) where x is not 11 or -11. It looks like it ought to be true for x=11 as well, except that at x=11, we have f(x)=0/0.

So, the function is continuous on

(-oo,-11) (-11,11) and (11,+oo)

While the limit from the left and right at x=11 is 1, the function is not continuous at x=11 because f(11) is not defined.