Newbetuts

Is it necessary for the codomain of the inner function to be equal to the domain of the outer function in function composition?

If $f: A\rightarrow B$ and $g: B\rightarrow C$ are surjective, then $g\circ f$ is surjective.

Big-O and function composition

For real univariate polynomials $f, g$, $f \circ f \circ f = g \circ g \circ g \implies f = g$?

Composition of two functions - Bijection

Every two positive integers are related by a composition of these two functions?

If $(f ∘ f)$ is differentiable, is $f$ also differentiable?

What numbers are in the set $S$?

Can it be that $f$ and $g$ are everywhere continuous but nowhere differentiable but that $f \circ g$ is differentiable?

Show that there exist a set $R$ and functions $β : S → R$ and $γ : R → T$ such that $β$ is onto, $γ$ is one-to-one and $α = γβ.$

Inverse of a composite function

Is there a multiple function composition operator? [duplicate]

Questions Regarding this Chain Rule Proof

Find $f(x)$ for $f(f(x))=\sin x$

What is composition of convex and concave function?

Why is this composition of concave and convex functions concave?

New posts in function-and-relation-composition

$R$ is transitive if and only if $ R \circ R \subseteq R$

Matrix Multiplication $\to$ Function Composition?

sigmoid $\circ$ sigmoid = sigmoid?

One-Way Inverse

Is it necessary for the codomain of the inner function to be equal to the domain of the outer function in function composition?

If $f: A\rightarrow B$ and $g: B\rightarrow C$ are surjective, then $g\circ f$ is surjective.

Big-O and function composition

For real univariate polynomials $f, g$, $f \circ f \circ f = g \circ g \circ g \implies f = g$?

Composition of two functions - Bijection

Every two positive integers are related by a composition of these two functions?

If $(f ∘ f)$ is differentiable, is $f$ also differentiable?

What numbers are in the set $S$?

Can it be that $f$ and $g$ are everywhere continuous but nowhere differentiable but that $f \circ g$ is differentiable?

Show that there exist a set $R$ and functions $β : S → R$ and $γ : R → T$ such that $β$ is onto, $γ$ is one-to-one and $α = γβ.$

Inverse of a composite function

Is there a multiple function composition operator? [duplicate]

Questions Regarding this Chain Rule Proof

Find $f(x)$ for $f(f(x))=\sin x$

What is composition of convex and concave function?

Why is this composition of concave and convex functions concave?