Four Zeros of a Reflected Difference

★ 7/10functions Absolute Value Casework Symmetry

Problem

Let

f(x)=\begin{cases}2-|x|,&x\leqslant 2,\\ (x-2)^2,&x>2,\end{cases}

and let $g(x)=b-f(2-x)$ with $b\in\mathbb R$ . If $y=f(x)-g(x)$ has exactly $4$ zeros, find the range of $b$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Absolute Value, Casework, Symmetry

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