Question: Please solve: Let f : R 4R oe a convex function. Let '7 E R be orbitmry. (a) Show that the level set L1, =

Please solve:

$Please solve: Let f : R\" 4R oe a convex$

Let f : R\" 4R oe a convex function. Let '7 E R be orbitmry. (a) Show that the level set L1, = {x E R\" | x) 5 7} is convex. (5) Give an example of a. function f that is not convex but it has convex level sets L? for any 7 > 0. The message from this exercise is that we cannot determine the convexity of a function by checking the convexity of its level sets

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