Does following funtion exists?
3922
How to prove that there exist no functions $f,g:\Bbb{R}\to\Bbb{R}$ such that $f(g(x))=x^{2018}$ and $g(f(x))=x^{2019}$?
24306
Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
153510
Questions about the existence of a function
90316
Do "Parabolic Trigonometric Functions" exist?
76249
Does the limit of function of two variables exist
61810
An application of Borel-Caratheodory theorem
40336
Existence of Holomorphic function (Application of Schwarz-Lemma)
16034
Function whose inverse is also its derivative?
2142
Finding a set of continuous functions with a certain property 2
53376
A continuous, nowhere differentiable but invertible function?
112548
Existence of non-trivial linear functional on any vector space
95694
Is there a name for the function $\max(x, 0)$?
57938
When do two functions become equal?
43667
Is $f(x,y(x))$ a function of two variables? If so, how is that possible?
37736
How to find a function in $ L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2 $
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 $L$?
28011
Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?