Prove that a given function is bijective
36941
If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?
14277
Proving $f(x)=x\cdot |x|$ is a bijection
2072
Demonstrate that if $f$ is surjective then $X = f(f^{-1}(X))$
148500
Understanding this theorem and how to go about proving it surjectivity?
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
82675
What is an example of function $f: \Bbb{N} \to \Bbb{Z}$ that is a bijection?
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
65977
Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
130381
bijection from $(a,b)$ to $\Bbb R$
74502
Proving the bijection of a continuous function $f$ such that $|f(x)-f(y)| \geq \log(1+|x-y|) \forall x,y$ in $\mathbb{R}.$
96202
Prove composition of bijections is bijection
59133
Show that an inverse of a bijective linear map is a linear map.
146436
Cardinality of the set of bijective functions on $\mathbb{N}$?
63146
Proof of properties of injective and surjective functions.
44689
Explicit bijection between $[0,1)$ and $(0,1)$
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
67451
Building a bijection from a finite union of countable sets to $\mathbb{N}$