I'm going through the examples provided in my textbook (Advanced Engineering Mathematics, 5th Edition) on Stokes theorem.
In the following example, I don't understand how $g(x, y, z) = z + x^2 -1$ was determined.
The function starts as $z = 1 - x^2$, which to my understanding would be a function of 2 parameters x, y, such that $f(x, y) = 1 - x$. I'm aware this can be rearranged to $0 = z + x^2 - 1$, but I don't understand the reason as to how $0$ can be replaced with $g(x, y, z)$. Would somebody please care to explain?