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pow:problem1

Problem 1 (due Monday, Feb. 17)

a) Is there a one-to one and onto function $f: (0,1)\longrightarrow (0,1)$ such that $f'=f^{-1}$, i.e. the derivative of $f$ equals the inverse of $f$?

b) Is there a one-to one and onto function $f: (0,\infty)\longrightarrow (0,\infty)$ such that $f'=f^{-1}$, i.e. the derivative of $f$ equals the inverse of $f$?

This problem was solved by only one participant: Yuqiao Huang. The submitted solution has been essentially the same as our “in-house” solution. To see the solution and some related open questions click the following link Solution