Limit of f(f(x)) at x=-2: Does it Exist?

[NATURE.M]

Consider the following
lim f(f(x))
x->-2

When looking at the graph of a function, if the function approaches -2 from above on the right
side, and approaches -2 from below on the left side, does the limit exist? I've been told it doesn't, but I don't understand why.

 

[arildno]

You need to specify what your function is.
If f(x)=x, for example, the limit certainly exists.

 

[NATURE.M]

Only the graph is given.

I guess you could suppose this is a similar graph.
http://curvebank.calstatela.edu/limit/grid3.gif

Then lim f(x) (lets suppose)
x->1

Since the function approaches from above on the right side , and below on the left side, does the limit exist??