# 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?