Is there a name for this kind of functions? $f(x,y) = z \iff x=g(y,z)$.

Question

Let $f : \mathbb R^2 \to \mathbb R$, if there exists $g: \mathbb R^2 \to \mathbb R$ such that, for all $x,y,z\in \mathbb R$, $$f(x,y)=z \iff x=g(y,z).$$ Is there a name for such $f$'s and is there a name for this $g$? I think this is somehow similar to the concept of inverse functions, but not identically the same.