How to prove that a function is injective
55175
Is the function $f(x) = x^2 - 2x$ one-to-one?
53551
$f(A\cap B)=f(A)\cap f(B)$ $\iff$ $f$ is injective.
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
42809
How can we show that $(I-A)$ is invertible?
49882
Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective
121395
Let $X$ and $Y$ be non-empty sets and let $f:X \rightarrow Y$. Prove that $ f^{ −1} :P(Y ) → P(X) $ is injective if, and only if, $f$ is surjective.
65977
Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
146356
To prove two sets are isomorphic is it sufficient to find 2 injections or 2 surjections?
13253
Prove $f(S \cup T) = f(S) \cup f(T)$
14277
Proving $f(x)=x\cdot |x|$ is a bijection
152013
elementary ring proof with composition of functions and addition of functions as operations
98118
Prove that a holomorphic function injective in an annulus is injective in the whole ball
33196
show that A(T) is a group under operation of composition of functions
148500
Understanding this theorem and how to go about proving it surjectivity?
117502
Proving that a certain continuous function is surjective.
112807
Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
34260
Injective function from $\mathbb{R}^2$ to $\mathbb{R}$?