functional analysis – The test map $ f: Bbb R ^ 2 to Bbb R ^ 3 $ is injective?

Leave $ V subset Bbb R ^ 2 $ be open, $ h: V to Bbb R $ differentiable and $ f: V to Bbb R ^ 3 $ $ (x, y) mapsto (x, y, h (x, y)) $

I want to show that f is injective.

I just wanted to know what / how can I do this? Jacobian? Implicit function theorem? Nullity-rank theorem?