Let $f:\mathbb{R}^n\to\mathbb{R}^n$ be continuously differentiable. Suppose there is a function $g:\mathbb{R}^n\to\mathbb{R}^n$ such that $fg=gf=1_{\mathbb{R}^n}$.
Does it follow that $g$ is differentiable?
Let $f:\mathbb{R}^n\to\mathbb{R}^n$ be continuously differentiable. Suppose there is a function $g:\mathbb{R}^n\to\mathbb{R}^n$ such that $fg=gf=1_{\mathbb{R}^n}$.
Does it follow that $g$ is differentiable?