Matematické Fórum

Marian · 07. 11. 2014 08:25 — Editoval Marian (07. 11. 2014 12:29)

Find at least one pair (if possible, find all pairs) of real functions $r(x)$ , $s(x)$ with the real variable x such that for all real x the following four conditions are satisfied:

(1) $r\circ s(x)=r(-x)$ ,
(2) $s\circ r(x)=-r(x)$ ,
(3) $r\circ r(x)=1$ ,
(4) $s\circ s(x)=\textnormal{sgn}\,(x)$ .

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Remark: The o-symbol means the composition of the functions, e.g., RoS(x):=R(t) where t:=S(x).

Matematické Fórum

#1 07. 11. 2014 08:25 — Editoval Marian (07. 11. 2014 12:29)

A pair of real functions

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