Question

(1)Given R={(x,y):x,y belongs to W,x²+y²​=25} Find the domain and range of R.

(2If R₁={(x,y)Iy=2x+7 where x belongs to R and -5 ≤x ≤5}is a relation.Then find the domain and range of R_1.

Answer 1

Dear student

R={(x,y):x,y belongs to W, x²+y²​=25}

$$\begin{gathered} x^2+y^2=25 \\ {y}^2=25-x^2 \\ y=\pm \sqrt{25-x^2} \\ Forytobedefined,termunderrootcannotbelessthanzero \\ 25-x^2\ge 0 \\ -5\le x\le 5 \\ andwhen,-5\le x\le 5then \\ 0\le x^2\le 25 \\ 0\le 25-x^2\le 25 \\ soyrangesfrom+5to-5 \\ asxandyarewholenumbers \\ Domainis\left\{-5,-4,-3,-2,-1,0,1,2,3,4,5\right\} \\ andrangeisalso\left\{-5,-4,-3,-2,-1,0,1,2,3,4,5\right\} \end{gathered}$$

Regards