Mathematics

Mathematics

Problem

Consider the function f(x)={−4−x2,−2≤x<01x−1,0<x≤4f(x)=\begin{cases}-\sqrt{4-x^{2}},& -2\le x<0\\ \dfrac{1}{x-1},& 0<x\le 4\end{cases} Which of the following represents the range of ff ? a) (−∞,0)∪[ 13,∞)(-\infty,0)\cup[\,\tfrac13,\infty) b) (−∞,0]∪[ 13,∞)(-\infty,0]\cup[\,\tfrac13,\infty) c) (−∞,0]∪(13,∞)(-\infty,0]\cup(\tfrac13,\infty) d) (−2,0]∪[ 13,∞)(-2,0]\cup[\,\tfrac13,\infty)

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