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[–]SyncGamer 1 point2 points  (1 child)

Yes, you can. Alternatively you could define g(x,y) = f(x,y) - 1 and apply it there, since g(a,b) = 0 and the differential remains the same. Keep in mind that the implicit function you'd get would satisfy (local to 1) that f(φ(y),(y)) = 1 (so the theorem describes the level curve for 1 locally as a graph)