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]

Let P,Q \in Z. Then for any t \in [0,1]

a = ta + (1-t)a \ge tf(P) + (1-t)f(Q) \ge f(tP + (1-t)Q)

Then tP + (1-t)Q \in X since X is convex, and so is in Z, and therefore Z is convex.

Less homework plox :3.