Question 1
Let
$$
A = \{ (x, y, z) \in \mathbb{R}^3 : xyz = 1,\ x + y + z = 3 \},
$$
under the function
$$
F(x, y, z) = xy + yz + zx.
$$
Determine the image of the set $A$ under $F$.
$$
A = \{ (x, y, z) \in \mathbb{R}^3 : xyz = 1,\ x + y + z = 3 \},
$$
under the function
$$
F(x, y, z) = xy + yz + zx.
$$
Determine the image of the set $A$ under $F$.