Proving a function is surjective given the composition is surjective
89514
Show that if $g \circ f$ is injective, then so is $f$.
33196
show that A(T) is a group under operation of composition of functions
152438
Is the composition of two injective functions injective?
20303
A function $f\colon E\to F$ between finite sets is injective iff it is surjective iff it is bijective
116732
Proving that a continuous map is surjective
28798
Proving injection and surjection with functions $F:C^B\to C^A$, $F(f)=f\circ\varphi$, $\varphi: A\to B$
133498
Show that Function Compositions Are Associative
117502
Proving that a certain continuous function is surjective.
40566
Counting surjective functions
21707
Constructing a Bijective function via an injective and surjective one.
88278
Show $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective
124523
Finding an Inverse Function and Composition of Functions?
35953
Prove that a function is not injective
115636
Show that $f$ is either injective or a constant function.
10024
How to prove $(f \circ\ g) ^{-1} = g^{-1} \circ\ f^{-1}$? (inverse of composition)
96202
Prove composition of bijections is bijection
10307
Show the inverse of a bijective function is bijective