If lim(x-->1) f(x)= 5, must f be defined at x=1

If it is, must f(1)=5? Can we conclude anything about the values of f at x=1? Explain.

Let f(x)=5 everywhere except x=1, and let f(1) be undefined. Then lim x->1 is 5 but f(1) is undefined.

Let f(x)=5 everywhere except x=1, and let f(1)=0. Then still lim x->1 is 5, since you can always find a neighborhood of 1 where f is as close as you like to 5.

Must f be defined at 1... no.
If it must, f(1) = 5... no.

You can't conclude anything about f(1), no.