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Question Number 24981 by tawa tawa last updated on 30/Nov/17

Commented by tawa tawa last updated on 30/Nov/17

$$\mathrm{please}\mathrm{help}.$$

Answered by kaivan.ahmadi last updated on 13/Dec/17

$$\mathrm{i}){2\mathrm{x}}^2-12\mathrm{x}+13=2({\mathrm{x}}^2-6\mathrm{x}+\frac{13}{2})=2({(\mathrm{x}-3)}^2-9+\frac{13}{2})=$$$$2({(\mathrm{x}-3)}^2-\frac{5}{2})=2{(\mathrm{x}-3)}^2-5$$

Answered by kaivan.ahmadi last updated on 13/Dec/17

$$\mathrm{ii})$$$$\mathrm{A}=6$$$$\mathrm{and}\mathrm{x}=3\mathrm{is}\mathrm{the}\mathrm{line}\mathrm{symmetry}$$

Answered by kaivan.ahmadi last updated on 13/Dec/17

$$\mathrm{iii})\mathrm{if}\mathrm{o}⩽\mathrm{x}⩽6\mathrm{then}$$$$\mathrm{Min}\left(\mathrm{y}\right)=2{(3-3)}^2-5=-5$$$$\mathrm{Max}\left(\mathrm{y}\right)=2{(0-3)}^2-5=13$$$${\mathrm{R}}_{\mathrm{f}}=[-5,13]$$

Answered by kaivan.ahmadi last updated on 13/Dec/17

$$\mathrm{y}=\mathrm{g}\left(\mathrm{x}\right)={2\mathrm{x}}^2-12\mathrm{x}+13=2({\mathrm{x}}^2-6\mathrm{x}+13/2)=$$$$2({(\mathrm{x}-3)}^2-9+13/2))=$$$$2({(\mathrm{x}-3)}^2-5/2))=2{(\mathrm{x}-3)}^2-5\Rightarrow$$$$\frac{\mathrm{y}+5}{2}={(\mathrm{x}-3)}^2\Rightarrow \mid \frac{\mathrm{y}+5}{2}\mid =\mathrm{x}-3,\mathrm{since}\mathrm{x}⩾4.$$$$\Rightarrow \mathrm{x}=\mid \frac{\mathrm{y}+5}{2}\mid +3\Rightarrow {\mathrm{g}}^{-1}\left(\mathrm{x}\right)=\mid \frac{\mathrm{x}+5}{2}\mid +3$$$$$$

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