Question 103
Define
$$
f(x, y, z) = \frac{(x y + y z + z x)(x + y + z)}{(x + y)(x + z)(y + z)}.
$$
Determine the set of real numbers $r$ for which there exists a triplet $(x, y, z)$ of positive real numbers satisfying $f(x, y, z) = r$.
$$
f(x, y, z) = \frac{(x y + y z + z x)(x + y + z)}{(x + y)(x + z)(y + z)}.
$$
Determine the set of real numbers $r$ for which there exists a triplet $(x, y, z)$ of positive real numbers satisfying $f(x, y, z) = r$.