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New posts in function-and-relation-composition
$R$ is transitive if and only if $ R \circ R \subseteq R$
elementary-set-theory
relations
equivalence-relations
function-and-relation-composition
Matrix Multiplication $\to$ Function Composition?
matrices
functions
function-and-relation-composition
sigmoid $\circ$ sigmoid = sigmoid?
functions
examples-counterexamples
function-and-relation-composition
One-Way Inverse
function-and-relation-composition
inverse-function
Is it necessary for the codomain of the inner function to be equal to the domain of the outer function in function composition?
functions
function-and-relation-composition
If $f: A\rightarrow B$ and $g: B\rightarrow C$ are surjective, then $g\circ f$ is surjective.
functions
proof-writing
solution-verification
function-and-relation-composition
Big-O and function composition
functions
asymptotics
computational-complexity
function-and-relation-composition
For real univariate polynomials $f, g$, $f \circ f \circ f = g \circ g \circ g \implies f = g$?
polynomials
function-and-relation-composition
Composition of two functions - Bijection
functions
function-and-relation-composition
Every two positive integers are related by a composition of these two functions?
elementary-number-theory
reference-request
prime-numbers
function-and-relation-composition
If $(f ∘ f)$ is differentiable, is $f$ also differentiable?
calculus
functions
derivatives
function-and-relation-composition
What numbers are in the set $S$?
number-theory
function-and-relation-composition
Can it be that $f$ and $g$ are everywhere continuous but nowhere differentiable but that $f \circ g$ is differentiable?
real-analysis
derivatives
continuity
function-and-relation-composition
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 $α = γβ.$
functions
function-and-relation-composition
Inverse of a composite function
algebra-precalculus
functions
solution-verification
inverse-function
function-and-relation-composition
Is there a multiple function composition operator? [duplicate]
notation
function-and-relation-composition
Questions Regarding this Chain Rule Proof
calculus
derivatives
chain-rule
function-and-relation-composition
Find $f(x)$ for $f(f(x))=\sin x$
functional-equations
function-and-relation-composition
What is composition of convex and concave function?
convex-analysis
function-and-relation-composition
Why is this composition of concave and convex functions concave?
convex-analysis
convex-optimization
function-and-relation-composition
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