Functions such that $f(g(x)) = x$ but $g(f(x)) \neq x $
126065
Example $g\circ f=id_A$ but $f\circ g\neq id_B$
153510
Questions about the existence of a function
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
127887
Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
25010
Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
28315
Monotone functions and non-vanishing of derivative
29403
Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
72254
Is that true that not every function $f(x,y)$ can be writen as $h(x) g(y)$?
106748
Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
50552
find functions that $f(m+k)=f(mk-n)$
14994
Showing a function $f$ cannot be surjective
156839
Functions Which are non differentiable on a Given Set.
4065
What are the entire functions $f$ such that $|f'(z)| \leq |f(z)| \ ? $