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Question Number 49983 by Tawa1 last updated on 12/Dec/18

$$\mathrm{Find}\mathrm{the}\mathrm{domain}\mathrm{of}\mathrm{the}\mathrm{function}\mathrm{and}\mathrm{sketch}\mathrm{the}\mathrm{graph}$$ $$\mathrm{f}\left(\mathrm{x}\right)=\{\begin{array}{l}2\mathrm{x}-1,\mathrm{if}\mathrm{x}<0\\ {\mathrm{x}}^2,\mathrm{if}0⩽\mathrm{x}⩽2\\ 1,\mathrm{if}\mathrm{x}⩽2\end{array}$$

Answered by kaivan.ahmadi last updated on 15/Dec/18

$$\mathrm{this}\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{function}\mathrm{since}\mathrm{f}(0.5)=0.25\mathrm{for}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2$$ $$\mathrm{and}\mathrm{f}(0.5)=1\mathrm{for}\mathrm{f}\left(\mathrm{x}\right)=1.$$ $$\mathrm{in}\mathrm{genral}\mathrm{the}\mathrm{domain}\mathrm{of}\mathrm{each}\mathrm{criterion}\mathrm{must}\mathrm{have}\mathrm{no}\mathrm{intersection}$$ $$\mathrm{otherwise}\mathrm{f}\mathrm{is}\mathrm{not}\mathrm{function}$$ $$(0⩽\mathrm{x}⩽2)\cap (\mathrm{x}⩽2)=[0,2]\ne \varnothing$$

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