Suppose that f: Rn †’ R and g: Rn †’ Rn are differentiable on Rn and that there exist r > 0 and a ˆˆ Rn such that Dg(x) is the identity matrix, I, for all x ˆˆ Br(a). Prove that there is a function h: Br(a) {a} †’ Br(x) such that

for all x ˆˆ Br(a) {a}.

Transcribed Image Text:

f (g(x))-f (g(a))l x - al