For $x \in \mathbb{R}^n$ and $A,B \in \mathbb{R}^{m \times n}$, $f(x) = ((Ax)^{2})^T((Bx)^2)$
where $^2$ denotes the power of 2, element-by-element of vector Ax or Bx. (I wasn't sure how to notate this)
Is $f(x)$ convex? How can it be shown?
If the domain of $x$ is restricted to be $x$ nonnegative, then is it convex?