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Omni-MATH / Find all functions f: mathbb R to mathbb R such that for any x,y in mathbb R, the multiset {(f(xf(y)+1),f(yf(x)−1)} is identical to the multiset {xf(f(y))+1,yf(f(x))−1}. [i]Note:[/…
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problem
Find all functions
$f: \mathbb R \to \mathbb R$ such that for any $x,y \in \mathbb R$, the multiset is identical to the multiset .
[i]Note:[/i] The multiset is identical to the multiset if and only if or .Plain-text mathematical notation (without MathML)
Find all functions $f: \mathbb R \to \mathbb R$ such that for any $x,y \in \mathbb R$, the multiset {(f(xf(y)+1),f(yf(x)−1)} is identical to the multiset {xf(f(y))+1,yf(f(x))−1}.
[i]Note:[/i] The multiset {a,b} is identical to the multiset {c,d} if and only if a=c,b=d or a=d,b=c.Original LaTeX notation
Find all functions $f: \mathbb R \to \mathbb R$ such that for any $x,y \in \mathbb R$, the multiset $\{(f(xf(y)+1),f(yf(x)-1)\}$ is identical to the multiset $\{xf(f(y))+1,yf(f(x))-1\}$.
[i]Note:[/i] The multiset $\{a,b\}$ is identical to the multiset $\{c,d\}$ if and only if $a=c,b=d$ or $a=d,b=c$.Discussion
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