Help needed on convex optimization!! 
Can some please help me in solving the below questions. I want to prove the below functions are convex, concave or neither.

Here are some useful facts:
Any norm is convex. If $f$ is convex and $T$ is affine then $g(x) = f(T(x))$ is convex. A conic combination of convex functions is convex. A maximum of convex functions is convex.
These rules can be used to prove the functions in your question are convex.
