Showing $f(x)=ax+b$ is a bijection for $a\ne 0$
100845
How to prove that $G(x)=ax+b$ is a one-to-one correspondence where $a\neq0$ and $a,b\in\mathbb{R}$.
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
22869
Prove $[0, 1]$ and $(0, 1]$ are equinumerous by use of bijection
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
23464
How to find a explicit bijection for some $f:A\times B \rightarrow B \times A$
26207
If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
102299
Bijection between $\mathbb{R}^n$ and $\mathbb{R}^m$
75266
$f(a+b)=f(a)+f(b)$ but $f$ is not linear
59133
Show that an inverse of a bijective linear map is a linear map.
48652
Solve the functional equation $2f(x)=f(ax)$ for some $a$.
15909
Bijection from $\mathbb R$ to $\mathbb {R^N}$
82675
What is an example of function $f: \Bbb{N} \to \Bbb{Z}$ that is a bijection?
149287
Prove that $A,B>0$ and $A_{ij}0$
35874
Show that when $BA = I$, the solution of $Ax=b$ is unique
14277
Proving $f(x)=x\cdot |x|$ is a bijection
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$