Is this morphism injective and surjective?

[Dominik Chodounsky]

f(x, y, z) = (√(x*y), √(x*z), √(y*z)) f: (R+)^3 -> (R+)^3


I think it's not surjectiove. For example for value (1, 2, 3), there are no positive real x, y, z which would get this value.


Is it injective? My intuition says that it is, but I'm not sure. How would I prove it?