Functions of several variables

Hi guys, we're just getting in to functions of several variables, and
I'm having trouble with one of the problems. Here it is:

Find a function f(x,y,z) whose level surface f=1 is the graph of the
function g(x,y)=x+2y

First, I set f=1, then if f(x,y,z) is a function, and g(x,y) is a
function, where g = f when f = 1, then the equation x+2y=z+1 should
represent the surface of f when z=0. So moving the variables over, I
end up with f(x,y,z)=x+2y-z-1, am I doing this correct? I have the
answer from the back of the book, it's a little different, I'll put it
in this thread if you want.

J
.