Let $f(x)=2-|x+1|$ for $-4\le x\le2$. The function $g$ is defined by $g(x)=\dfrac{1}{f(x)}$

Question

Let $f(x)=2-|x+1|$ for $-4\le x\le2$. The function $g$ is defined by $g(x)=\dfrac{1}{f(x)}$ wherever $f(x)\ne0$. Determine the range of $g$, giving your answer as a union of intervals.

Accepted Answer

$(-\infty,-1]\cup\left[\dfrac12,\infty\right)$

Reciprocal range of an off-centre modulus peak

Reciprocal range of an off-centre modulus peak

Solution:

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