If , then [MATH%
first think in two dimensions. means although it may not always be possible to express as an explicit function of x.
similarly means . Again it may not always be possible to express explicitly as a function of and .
Geometrically is a function of 3 independant variable. there is no constraint on the values of (except that these must lie in the domain of the definition of the function). if you set equal to zero you have effectively put 1 constraint, that is, if you choose arbitrary values of then the value of should be so that the function must become zero. now since becomes fixed when is a point chosen(anywhere in the domain) on - plane, the equation is that of a surface.
For the sake of understanding suppose we could write we have .
if is a constant then
which on using we have,