Question 66
Let $S$ be the set of positive real numbers. Find all functions $f:S^3\to S$ such that, for all positive real numbers $x,y,z,k$:
(a) $xf(x,y,z)=zf(z,y,x)$;
(b) $f(x,yk,k^2z)=kf(x,y,z)$;
(c) $f(1,k,k+1)=k+1$.
Problem (Romanian source version):
Let $S$ be the set of strictly positive real numbers. Find all functions $f:S^3\to S$ satisfying
(a) $xf(x,y,z)=zf(z,y,x)$;
(b) $f(x,yk,k^2z)=kf(x,y,z)$;
(c) $f(1,k,k+1)=k+1$,
for every choice of strictly positive real numbers $x,y,z,k$.
(a) $xf(x,y,z)=zf(z,y,x)$;
(b) $f(x,yk,k^2z)=kf(x,y,z)$;
(c) $f(1,k,k+1)=k+1$.
Problem (Romanian source version):
Let $S$ be the set of strictly positive real numbers. Find all functions $f:S^3\to S$ satisfying
(a) $xf(x,y,z)=zf(z,y,x)$;
(b) $f(x,yk,k^2z)=kf(x,y,z)$;
(c) $f(1,k,k+1)=k+1$,
for every choice of strictly positive real numbers $x,y,z,k$.