Evelyn Freeman

Evelyn Freeman

Answered

2022-10-20

How to show that f 1 ( I ) is convex if that is indeed the case?

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Recalculate according to your conditions!

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veirenca77

veirenca77

Expert

2022-10-21Added 9 answers

The answer is no. Consider f : R R given by f ( x ) = x 2 . We know that f 1 ( [ 4 , 16 ] ) = [ 4 , 2 ] [ 2 , 4 ], which is disconnected and so not convex.
On the other hand, if f is concave, then its super-level sets are convex. That is, f 1 ( [ c , ) ) is always convex, as you already noted.

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