Proof that if the Composition of g and f is one-to-one and f is onto, then g is one to one
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is injective
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
65744
How can I Prove that H=G or K=G
100845
How to prove that $G(x)=ax+b$ is a one-to-one correspondence where $a\neq0$ and $a,b\in\mathbb{R}$.
25050
To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
130363
Prove composition of two surjections is surjection
110313
Prove that $\gcd(f(x),g(x)) = 1$.
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
22248
$G$ solvable $\implies$ composition factors of $G$ are of prime order.
110142
1-1 Function Composition
62455
Prove Equivalence Relation in G
133699
Proving that there is a bijection between $A$ and $B$.
104757
If $f \circ g$ is surjective, then f is surjective
10859
Prove $\sup(f+g) \le \sup f + \sup g$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
58642
If $g \circ f$ is the identity function, then which of $f$ and $g$ is onto and which is one-to-one?
82935
Prove that f∈Θ(g)if and only ifO(f) =O(g).