Solution
= Solution
The map $u\mapsto u^2$ is <strictly increasing> on $[0,\infty)$: for $u,v\ge0$, $u\le v$ if and only if $u^2\le v^2$. Therefore a point has the smallest $f$-value if and only if it has the smallest $f^2$-value, and the same applies to $g$. By <minimizers under strictly increasing transformations>, \b[both asserted <argmin> equalities hold], including when the <argmin> sets are empty. The differentiability assumptions are unnecessary for this order argument.