How do I solve this limit

Question

**Find the limit ${x \to 6}$ if $ f(f(x))$ **

Any idea how to solve this graphical question on limits?

Answer 1

Hint:

In a neighborhood of 6 $f(x)$ is continuous and we have $f(x)>2$ , so :

$$ \lim_{x \rightarrow 6}f(f(x))= \lim _{f(x) \rightarrow 2^+} f(f(x))=\lim _{y \rightarrow 2^+} f(y) $$ and you can see this limit from the graph.