Typo in Spivak Calculus on Manifolds?

Question

In the proof of theorem 5.2 of Spivak's calculus on manifolds, he invokes the inverse function theorem for a function g that he defines there without ever assuming that it was continuously differentiable. Is this a typo?

Answer 1

The function $g$ is defined as $$g(a,b)=f(a)+(0,b)$$ with $f$...