New posts in Function And Relation Composition

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

What is this property called for a function? $f(f(x))=f(x)$

If $(f\circ g)(x)=x$ does $(g\circ f)(x)=x$?

If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?

Big-O and function composition

composition of two uniformly continuous functions.

Real Analysis: Continuity of a Composition Function

Show that Function Compositions Are Associative

half iterate of $x^2+c$

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