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]

>>7
Ah, I get it now, thanks bro. But that question was just a warm up.

Prove also that if \left\{ f_i \right\}_{i \in I} is a collection of convex functions on a convex subset X \subseteq \Re^n and \left\{ a_i \right\}_{i \in I} is a collection of real numbers, then the set \left\{ x \in X \mid f_i(x) \leq c_i, \forall i \in I\right\} is a convex subset of \Re^n.