Let $V$ be a real [vector space](/page/Vector%20Space), let $C \subset V$ be convex, and let $J \subset \mathbb{R}$ be an interval. Let $f:C\to\mathbb{R}$ be a [convex function](/page/Convex%20Function) such that $f(C)\subset J$, and let $g:J\to\mathbb{R}$ be convex and nondecreasing. Then the composition