0
Is there a function / Are there such functions $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(f(x))=x^2-2$?
My Solution:
\begin{align}
&\text{Let's look for $t_2$ which satisfies } f^2(t_2)=t_2. \\
&\Rightarrow t_2=2, -1. \\
\ \\
&\text{Now, let's look for $t_4$ which satisfies } f^4(t_4)=t_...
In mathematics, a functional square root (sometimes called a half iterate) is a square root of a function with respect to the operation of function composition. In other words, a functional square root of a function g is a function f satisfying f(f(x)) = g(x) for all x.
== Notation ==
Notations expressing that f is a functional square root of g are f = g[1/2] and f = g1/2.
== History ==
The functional square root of the exponential function (now known as a half-exponential function) was studied by Hellmuth Kneser in 1950.
The solutions of f(f(x)) = x over
R...
