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Question Number 107452 by Rio Michael last updated on 10/Aug/20

$$\mathrm{Given}\mathrm{a}\mathrm{function}f\mathrm{which}\mathrm{is}\mathrm{periodic}\mathrm{of}\mathrm{period}2\mathrm{defined}\mathrm{by}$$ $$f\left(x\right)=\{\begin{array}{l}3x^2-4,\mathrm{if}0⩽x<3\\ x-3,\mathrm{if}3⩽x<6\end{array}$$ $$\left(1\right)\mathrm{State}\mathrm{in}\mathrm{a}\mathrm{similar}\mathrm{manner}f{}^{\prime }\left(x\right).$$ $$\left(2\right)\mathrm{Check}\mathrm{if}f\mathrm{is}\mathrm{continuous}.$$ $$\left(3\right)\mathrm{find}f\left(7\right)\mathrm{and}\mathrm{skech}\mathrm{the}\mathrm{curve}y=f\left(x\right).$$

Answered by 1549442205PVT last updated on 11/Aug/20

$$\mathrm{The}\mathrm{periodic}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)\mathrm{of}\mathrm{period}\mathrm{T}$$ $$\mathrm{is}\mathrm{a}\mathrm{function}\mathrm{that}\mathrm{satisfy}$$ $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}(\mathrm{x}+\mathrm{T})\mathrm{\forall }\mathrm{x}\in {\mathrm{D}}_{\mathrm{f}}({\mathrm{D}}_{\mathrm{f}}-\mathrm{the}\mathrm{defined}$$ $$\mathrm{domain}\mathrm{of}\mathrm{f}\left(\mathrm{x}\right)).\mathrm{The}\mathrm{above}\mathrm{function}$$ $$\mathrm{has}\mathrm{no}\mathrm{that}\mathrm{property}\mathrm{sir}?$$

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