$f (f(x))=-x$ - there's no such function
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
144773
function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct?
26677
thoughts about $f(f(x))=e^x$
87041
How to determine with certainty that a function has no elementary antiderivative?
14994
Showing a function $f$ cannot be surjective
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
83338
Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
103568
Possibility of finding a such function?
151519
If $f(f(x))=x^2-x+1$, what is $f(0)$?
76679
Prove there are no other solutions of functional equation $f(x+y) = \frac{f(x)+f(y)}{1-f(x)f(y)}$
6482
Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?
31269
How to visualize $f(x) = (-2)^x$
127921
Does there exist a function such that $\lim_{x \to a} f(x) = L$ for all $a \in \mathbb R$ but $f(x)$ is never $L$?
151958
How to show $f'(0)$ exist and is equal to $1$?
1071
Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
153510
Questions about the existence of a function