Question Number 52610 by Kunal12588 last updated on 10/Jan/19
![please help me y=(√(9−x^2 )) Q find domain and range of given real function i found the domain=[−3,3] but for range i followed this way y^2 =9−x^2 x^2 =9−y^2 ⇒x=(√(9−y^2 ))⇒y=[−3,3] but the answer is [0,3] after checking the graph y≥0. yes its true we have to take positive root but how can i write it](https://www.tinkutara.com/question/Q52610.png)
$$\:{please}\:{help}\:{me} \\ $$$${y}=\sqrt{\mathrm{9}−{x}^{\mathrm{2}} } \\ $$$${Q}\:{find}\:{domain}\:{and}\:{range}\:{of}\:{given}\:{real}\:{function} \\ $$$${i}\:{found}\:{the}\:{domain}=\left[−\mathrm{3},\mathrm{3}\right] \\ $$$${but}\:{for}\:{range}\:{i}\:{followed}\:{this}\:{way} \\ $$$${y}^{\mathrm{2}} =\mathrm{9}−{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} =\mathrm{9}−{y}^{\mathrm{2}} \Rightarrow{x}=\sqrt{\mathrm{9}−{y}^{\mathrm{2}} }\Rightarrow{y}=\left[−\mathrm{3},\mathrm{3}\right] \\ $$$${but}\:{the}\:{answer}\:{is}\:\left[\mathrm{0},\mathrm{3}\right] \\ $$$${after}\:{checking}\:{the}\:{graph}\:\:{y}\geqslant\mathrm{0}.\:{yes}\:{its}\:{true} \\ $$$${we}\:{have}\:{to}\:{take}\:{positive}\:{root}\:{but}\:{how}\:{can}\:{i} \\ $$$${write}\:{it} \\ $$
Commented by Kunal12588 last updated on 10/Jan/19
$${offcourse}\:{sir}\:{but}\:{tommorow}\:{is}\:{my}\:{test}\:{i}\:{can}'{t} \\ $$$${draw}\:{graphs}\:{their} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 10/Jan/19
$${to}\:{my}\:{view}\:{it}\:{is}\:{better}\:{to}\:{cosults}\:{graph}\:…{available} \\ $$$${in}\:{playstore}…{some}\:{questions}\:{easily}\:{understood} \\ $$$${from}\:{graph}… \\ $$$$ \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 10/Jan/19
Commented by Kunal12588 last updated on 10/Jan/19
$${thank}\:{you}\:{sir} \\ $$
Answered by kaivan.ahmadi last updated on 10/Jan/19
$$\mathrm{since}\:\mathrm{y}=\sqrt{\mathrm{9}−\mathrm{x}^{\mathrm{2}} \:}\:\mathrm{so}\:\mathrm{y}\geqslant\mathrm{0}\:.\mathrm{it}\:\mathrm{means}\:\mathrm{min}\left(\mathrm{y}\right)=\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{found}\:\mathrm{max}\left(\mathrm{y}\right) \\ $$$$\mathrm{y}\:\mathrm{is}\:\mathrm{max}\:\mathrm{when}\:\mathrm{9}−\mathrm{x}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{max}\: \\ $$$$\mathrm{so}\:\mathrm{max}\left(\mathrm{y}\right)=\sqrt{\mathrm{9}}=\mathrm{3} \\ $$
Commented by Kunal12588 last updated on 10/Jan/19
$${thank}\:{you}\:{sir} \\ $$