1. For each of the following functions, prove that

f- 1 exists and is differentiable in some nonempty, open set containing

(a, b), and compute D(f-1 )

(a, b)

(a) f(u, v) = (3u - v, 2u + 5v) at

(a, b).

(b) f(u,v) = (u+v,sinu+cosv) at (a,b) = (0,1).

(c) f(u, v) = (uv, u2 + v2) at

(a,

b) = (2,5).

(d) f(u,v) = (u3 -v2,sinu-Iogv) at (a,b) = (-1,0).