If $f\circ g$ is injective then $g$ is injective
74453
Injective and Surjective Functions
89514
Show that if $g \circ f$ is injective, then so is $f$.
27366
Prove that $g$ is tangent to the graph of $f$
46863
Show that $g$ is injective
2093
If $f$ is continuous then $G$ is homeomorphic to $X$.
141166
How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$ is injective, then $\phi$ is also injective?
104757
If $f \circ g$ is surjective, then f is surjective
101042
Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
157378
On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
25997
Conditions Equivalent to Injectivity
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$
85612
Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
75473
If a group $G$ has odd order, then the square function is injective.
14277
Proving $f(x)=x\cdot |x|$ is a bijection