Do there exist functions such that $f(f(x)) = -x$?
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
17154
Does a non-trivial solution exist for $f'(x)=f(f(x))$?
106830
are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
27960
Is there a name for function with the exponential property $f(x+y)=f(x) \cdot f(y)$?
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
85282
Will inverse functions, and functions always meet at the line $y=x$?
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
106748
Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
6636
Is there a positive function $f$ on real line such that $f(x)f(y)\le|x-y|, \forall x\in \mathbb Q , \forall y \in \mathbb R \setminus \mathbb Q$?
81799
Examples of functions where $f(ab)=f(a)+f(b)$
77180
In pure functional languages, is there an algorithm to get the inverse function?
144773
function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct?
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
107400
Can there be an injective function whose derivative is equivalent to its inverse function?