Let $f: A\rightarrow A$. Prove that if $(f ◦ g)$ is surjective, then $f$ is surjective.
104757
If $f \circ g$ is surjective, then f is surjective
45792
Rigorous proof that surjectivity implies injectivity for finite sets
20199
Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
14994
Showing a function $f$ cannot be surjective
148616
When is a ring homomorphism $A \to A$ surjective but not injective.
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
88928
$F:G\to B$ is an isomorphism between groups implies $F^{-1}$ is an isomorphism
125644
How to check f is surjective
56278
$I$ and $J$ are coprime ideals iff $x \to (x + I, x + J)$ is surjective.
106809
$f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
85768
The function $f:G \rightarrow G$ defined by $f(x)=x^2$ is a homomorphism iff G is abelian.
74657
Can this intuition give a proof that an isometry $f:X \to X$ is surjective for compact metric space $X$?
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
116732
Proving that a continuous map is surjective
136842
$|x-f(x)|<5777$, Show that $f$ is surjective
46748
If $g \circ f$ is surjective, show that $f$ does not have to be surjective?
74453
Injective and Surjective Functions