I am given the limit bellow. How do I solve this problem? I am thrown off by the f(f(x)). I believe the answer is -2 but am not sure and would like an explanation.
2026-03-26 08:03:46.1774512226
How to solve limit whose function uses another function as a parameter?
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If $x \le -2$ then $f(x) = 2$. And $f(2) = -1$.
For any $\epsilon > 0$ if $\delta = 1$ then $|x-(-3)| < \delta \implies -4 < x < -2\implies f(x) = 2 \implies f(f(x)) =-1$ and $|f(f(x)) - (-1)| = |f(2) - (-1)| = |(-1)-(-1)| = 0 < \epsilon $.
And that is the very definition of $\lim\limits_{x\to -3} f(f(x)) = -1$.