Prove that a function $f:\mathbb R \to\mathbb R$ given by $f(x) = x\left|x\right|$ is a bijection
14277
Proving $f(x)=x\cdot |x|$ is a bijection
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
10253
Proving that all entire & injective functions take the form $f = ax + b$?
130381
bijection from $(a,b)$ to $\Bbb R$
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
117716
Condition on function $f:\mathbb{R}\rightarrow \mathbb{R}$ so that $(a,b)\mapsto | f(a) - f(b)|$ generates a metric on $\mathbb{R}$
14322
Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
16109
Prove that $ \int _a^b\:f\left(x\right)\:\:dx\:=\:\int _a^b\:f\left(a+b-x\right)\:\:dx $
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
53101
Is it true that the relation |A| < |B| is a sufficient condition for claiming that $f$ is a bijection?
28692
Find if set $I$ of all injective functions $\mathbb{N} \rightarrow \mathbb{N}$ is equinumerous to $\mathbb{R}$
124374
A bijective function between a square and its side
34077
Let $f:\mathbb{R}\to\mathbb{R}$ satisfy $f\big(x-f(y)\big)=f\big(f(y)\big)+x\cdot f(y)+f(x)-1$ for all $x,y\in\mathbb{R}$.