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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §4.3 Inverse Functions and Their Derivatives, #29 · Calculus · Differentiation rules

The slopes of … and … are … and

The slopes of $f (x) = \frac{1}{3} x^{3}$ and $g (x) = - 1/ x$ are $x^{2}$ and $1/ x^{2}$ . Why isn't $f = g^{- 1}$ ? What is $g^{- 1}$ ? Show that $g^{'} (g^{- 1}) = 1$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §4.3 Inverse Functions and Their Derivatives, #29

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