From an explicit function to an implicit one

Question

I've seen a lot of people asking questions about how to go from an implicit expression and get an explicit function. I wonder if we can do the opposite: starting with an explicit function $d(x,y)$ and write this in a implicit form. I think we should simply consider
$$f(x,y,z)= z- d(x,y)$$ but I'm not sure if this is the idea behind the problem.