A Max of Two Linear Forms

★ 6/10functions Extrema Absolute Value inequality

Problem

Define $\max\{a,b\}=\begin{cases}a,&a\geqslant b,\\ b,&a<b.\end{cases}$ Real numbers $x,y$ satisfy $|x|\leqslant 2$ and $|y|\leqslant 2$ . Find the range of

z=\max\{4x+y,\;3x-y\}.

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, Absolute Value, inequality

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