So I have this question here. Obviously, I don't think I am expected to take a composition of a function 10 times. That would be crazy. My idea is that f(x) repeats 10 times and that $\sqrt{2}$ repeats 10 times too so I was thinking I could write $f(x)$ as:
$$f(x)=\sqrt{2^{(1/2)^{10}}(f(x))^{10}+17}-3.$$ I could then go from there or something. Anything to add? Am I completely off or am I doing something totally wrong?
Note that $f(2)=2$ and $f(4)=4$. Moreover $f$ is a continuous and strictly increasing function in $[2,4]$. These properties hold also for the composition $g$. Therefore $g((2,4))=(2,4)$ and by the Intermediate Value Theorem there is $c\in (2,4)$ such that $g(c)=3$. Note that since $g$ is strictly increasing the point $c$ is unique.