Dominating an Absolute Difference

★ 5/10functions Absolute Value inequality Casework

Problem

Let $f(x)=2|x+1|-|x-2|$ .

1. Solve the inequality $f(x)\leqslant 0$ . 2. Let $g(x)=|3x-a|$ . If $g(x)\geqslant f(x)$ for all $x\in\mathbb R$ , find the range of $a$ .

Answer

Solution

Difficulty	5/10
Topics	functions, Absolute Value, inequality, Casework

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