I need help. For which $(r, θ, φ) ∈ \mathbb{R}^3$ is the function $$f(r,\theta,\varphi)=\begin{pmatrix}x(r,\theta,\varphi)\\ y(r,\theta,\varphi)\\z(r,\theta,\varphi)\end{pmatrix}=\begin{pmatrix}r\sin \theta\cos \varphi \\ r\sin \theta \sin \varphi \\ r\cos \theta\end{pmatrix} $$
locally reversible? and calculate $(f^{-1})'(0, -7, 0)$.