For $-2\le x\le3$, define $p(x)=|2x-1|-3$ and $q(x)=\dfrac{1}{p(x)}$ wherever \(p(x)\ne0\

Question

For $-2\le x\le3$, define $p(x)=|2x-1|-3$ and $q(x)=\dfrac{1}{p(x)}$ wherever $p(x)\ne0$. The range of $q$ is $\{y:y\le a\text{ or}\hspace{0.5em}y\ge b\}$. Find the exact values of $a$ and $b$.[4]

Accepted Answer

$a=-\dfrac13,\ b=\dfrac12$

Reciprocal range of a stretched modulus trough

Reciprocal range of a stretched modulus trough

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