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Question Number 83653 by jagoll last updated on 05/Mar/20

$$\mathrm{find}\mathrm{range}\mathrm{of}\mathrm{function}$$$$\mathrm{y}=\frac{4}{(x^2-4)}$$

Answered by MJS last updated on 05/Mar/20

$$x=\pm 2\sqrt{\frac{y+1}{y}}$$$$\Rightarrow y⩽-1\vee y>0$$

Commented by jagoll last updated on 05/Mar/20

$$\mathrm{yess}$$

Answered by jagoll last updated on 05/Mar/20

$$\mathrm{domain}x\ne \pm 2$$$$\iff x^2-4=\frac{4}{y}\Rightarrow x=\pm \sqrt{4+\frac{4}{y}}$$$$x=\pm \sqrt{\frac{4\mathrm{y}+4}{\mathrm{y}}},\frac{4\mathrm{y}+4}{\mathrm{y}}⩾0$$$$\mathrm{y}⩽-1\vee \mathrm{y}>0$$

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