You should be able to...

Let [IEQ]X \subseteq \Re ^n[/IEQ] be a convex subset. Let [IEQ]f: X \rightarrow \Re [/IEQ] be a convex function. Prove for any [IEQ]a \in \Re[/IEQ], [IEQ]Z = \left\{x\in X \mid f(x) \leq a  \right\} [/IEQ] is a convex subset of [IEQ]\Re ^n[/IEQ]

>>4
I don't see how you get the first inequality.