As the question asks (though rather vaguely), what is the nth iteration of $f(x)$ such that $f(x)=x^2+c$? I've attempted to find a solution to this by referring to this wikipedia article: https://en.wikipedia.org/wiki/Iterated_function#Definitions_in_terms_of_iterated_functions
Specifically, I tried to use the method shown in the section "some formulas for fractional iteration" and that simply got me nowhere, because I'm having trouble with the part where you use the nth derivative of f(x) evaluated at a fixed point.
Then, I tried to find some kind of homeomorphism. If you have the function $f(x)=x^2-2$ which is of the form $f(x)=x^2+c$, you can easily define a function $\phi(x)=x+\frac{1}{x}$ and show that $f(\phi(x)))=\phi(x^2)$, then do fancy algebra and function stuff to find what $f^n(x)$ is. I was wondering if I could do something similar for the case of any $c$, but I haven't gotten anywhere.
And so I've come here, wondering if anyone could offer some insight for all of this.