Let

$($a$)$ ?Show that the equation f$($X$,$y$,$z$)=0$ ?defines z as a function z $=$ ?z$($x$,$y$)$ ?in a neighborhood of P$.$ ?

$($b$)$ ?State the equation of the tangent plane to the surface f$($x$,$y$,$z$)=0$ ?in P 

$($c$)$ ?Determine the shortest distance between the plane from $($b$)$ ?and the point $(1,-1,1)$ ?using Lagrange's method

re+cos(2)-8 och P= (2,0,/2).