Actually I think there is a major flaw in this part of the explanation It refers to the graphic and talks about visualizing the contour lines of both f and g but the graphic only shows the contour of f in blue The red line for gxyc is not the contour line of g If it were all its points would have the same height z coordinate equal to c but they vary in height The red line is in fact the set of points  xyfxy  gxyc  The contour line of gxy  c is instead the set  xyc  gxyc