Is there a simpler expression for $f(f(f(...f(x)...)))$ (total n '$f$')?
72570
Notation for repeated application of function
77074
If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
103706
If $\{f(0)\}^{2} + \{f'(0)\}^{2} = 4$ then there is a $c$ with $f(c) + f''(c) = 0$
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
55485
Recursive Function - $f(n)=f(an)+f(bn)+n$
23222
If $f(x) + f'(x) + f''(x) \to A$ as $x \to \infty$, then show that $f(x) \to A$ as $x \to \infty$
98933
Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$
106013
Given $f(x) = x + |x|$ for what values of $x$ is $f$ differentiable
32575
What's the name for the property of a function $f$ that means $f(f(x))=x$?
8913
Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
62504
Is there any known relationship between $\sum_{i=1}^{n} f(i)$ and $\sum_{i=1}^{n} \dfrac {1}{f(i)}$
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
25563
Count number of increasing functions, nondecreasing functions $f: \{1, 2, 3, \ldots, n\} \to \{1, 2, 3, \ldots, m\}$, with $m \geq n$.
28927
IMO 1987 - function such that $f(f(n))=n+1987$
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
51291
How can I express $\int \frac{1}{f'(x)}$ in terms of $f(x)$