Let be a convex function on a convex domain and a convex non-decreasing function on . Prove that the composition of is convex on .

**Solution**

We want to prove that for it holds that

We have:

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Let be a convex function on a convex domain and a convex non-decreasing function on . Prove that the composition of is convex on .

**Solution**

We want to prove that for it holds that

We have: