Functions satsify $f'=f^{-1}$ with $f^{-1}$ is compostional inverse of$ f$
16034
Function whose inverse is also its derivative?
62067
Inverse function of $x^x$
47166
Is there a function whose inverse is exactly the reciprocal of the function, that is $f^{-1} = \frac{1}{f}$?
52701
Manipulating Partial Derivatives of Inverse Function
150274
Inverse of a function - $f^-(x)$ in a restricted domain
124523
Finding an Inverse Function and Composition of Functions?
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
99179
Continuous function with compact domain has continuous inverse
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
30860
Prove that $f(x)=0$ in $[-1,1]$.
104263
How to show that $f'(x)<2f(x)$
36093
Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
59063
$f(f(x))=f(x)$ question
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$
61640
Prove c exists for f:[0,1] -> R
13193
Does a inverse function need to be either surjective or injective?