Newbetuts

Operational details (Implementation) of Kneser's method of fractional iteration of function $\exp(x)$?

Are there two functions $f, g$ such that $f(g(x)) = x^3$ and $g(f(x)) = x^5$?

Notation for repeated composition of functions

Fractional Composite of Functions

Can the Identity Map be a repeated composition one other function?

composition of two uniformly continuous functions.

$f(f(x))=f(x)$ question

How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)

Show that Function Compositions Are Associative

Given $g(x)$ and $f(g(x))$, solve for $f(x)$.

Which functions satisfy $f^n(x) = f(x)^n$ for some $n \ge 2$?

Characterising functions $f$ that can be written as $f = g \circ g$?

What numbers can be created by $1-x^2$ and $x/2$?

Real Analysis: Continuity of a Composition Function

half iterate of $x^2+c$

New posts in function-and-relation-composition

Limit Laws for Composite Functions

If $f \circ g$ is onto then $f$ is onto and if $f \circ g$ is one-to-one then $g$ is one-to-one

If $g \circ f$ is surjective, show that $f$ does not have to be surjective?

Why any countable subset of $\mathbb{R}→\mathbb{R}$ is generated by a finite set under composition?

If the absolute value of a function is continuous, is the function continuous?

Operational details (Implementation) of Kneser's method of fractional iteration of function $\exp(x)$?

Are there two functions $f, g$ such that $f(g(x)) = x^3$ and $g(f(x)) = x^5$?

Notation for repeated composition of functions

Fractional Composite of Functions

Can the Identity Map be a repeated composition one other function?

composition of two uniformly continuous functions.

$f(f(x))=f(x)$ question

How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)

Show that Function Compositions Are Associative

Given $g(x)$ and $f(g(x))$, solve for $f(x)$.

Which functions satisfy $f^n(x) = f(x)^n$ for some $n \ge 2$?

Characterising functions $f$ that can be written as $f = g \circ g$?

What numbers can be created by $1-x^2$ and $x/2$?

Real Analysis: Continuity of a Composition Function

half iterate of $x^2+c$