\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(f : ]0, +\infty[ \to ]0, +\infty[\), \(f(x) = 1/x\). Show that \(f\) is a \(C^\infty\) bijection and that \(f^{-1} = f\). Since \(f^{-1} = f\), the inverse-map derivative formula reduces to \(f'(x) \cdot f'(f(x)) = 1\) --- verify this identity directly.
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.