I have to compute the convex conjugate (Fenchel) and the subgradients for the following two functions:
$\boxed{f_1:[-1,1]\rightarrow \mathbb{R}:x\mapsto 0}$ and
$\boxed{f_2:\{x\in \mathbb{R}^2:||x||_2\leq 1\}\rightarrow \mathbb{R}:x\mapsto 0}$
I have done this for different functions so far which seems much more complicated than this. So I'm not sure if understand this problem right. The functions are differentiable in every $x$, so the subgradients are equal to the gradients. For both function this is 1. Is this right? What about the convex conjugate? I have no idea how to start this here. Any help appreciated.