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

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 $\{y:y\le a\text{ or }y\ge b\}$. Find the exact values of $a$ and $b$.

Accepted Answer

$a=-\tfrac13,\ b=\tfrac12$

Reciprocal range of a stretched modulus trough

Reciprocal range of a stretched modulus trough

Solution:

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