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Question Number 94078 by Rio Michael last updated on 16/May/20

$$\mathrm{Given}\mathrm{the}\mathrm{function}f\mathrm{defined}\mathrm{by}f\left(x\right)=\frac{\mid x-2\mid }{1-\mid x\mid }$$ $$\left(\mathrm{i}\right)\mathrm{state}\mathrm{the}\mathrm{domain}\mathrm{of}f.$$ $$\left(\mathrm{ii}\right)\mathrm{show}\mathrm{that}$$ $$f\left(x\right)=\{\begin{array}{l}\frac{2-x}{1+x},x<0\\ \frac{2-x}{1-x},0⩽x<2\\ \frac{x-2}{1-x},x⩾2\end{array}$$ $$\left(\mathrm{iii}\right)\mathrm{Investigate}\mathrm{the}\mathrm{continuity}\mathrm{of}f\mathrm{at}x=2.$$

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