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My question is that let’s say I have a concave increasing function, can I transform it into a new convex increasing function? I know you can take log or exp of the function till it changes one to another, but I mean in a more generic and certain way.

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  • $\begingroup$ What do you mean by transform? The question doesn't really make sense as stated. $\endgroup$ – copper.hat Aug 5 '18 at 14:05
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Here is one idea, surely not what you intended. Negation flips about the horizontal, changing concave to convex. Reflecting in a vertical line $x=c$ then turns convex decreasing to convex increasing. Shifting vertically with constants retains these properties.


          ConcConv
          $3+x^2$ is concave increasing, $10-x^2$ is convex decreasing. $10-(x-4)^2$ reflects around the vertical $x=4$.


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