I find it always helpful to think of a function as a function of a certain number of independent variables. In this case, f is a function of one variable. I know it's got an x and a y in there, but if it were a function of two variables, I think you'd write as f(x,y) = g(xy), and even then, g would be a function of only one variable. How can that be? Because you could write a new variable u = xy, and then say that z = f(u).
Hence, I think, rather, that
and so on. Does that make sense?