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Can't understand how the function g is created;why (x-1) (x+2) ??why they are squared? why they are less or equal to 1 and 1/4??

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    $\begingroup$ The region inside a disc with center $(h,k)$ and radius $r$ is given by $(x-h)^2+(y-k)^2=r^2$ (Why? Hint: distance formula) $\endgroup$ – Kenny Lau May 3 '17 at 16:31
  • $\begingroup$ Write it as $\|(x,y)-(1,0)\|^2 \le 1$ or $\|(x,y)-(-2,0)\|^2 \le {1 \over 4}$. $\endgroup$ – copper.hat May 3 '17 at 16:32
  • $\begingroup$ These are just standard equations of a circle $(x-h)^2 + (y-k)^2 = r^2$ which denotes a circle of radius r centered at the point $(h,k)$. An inequality means you also have the inside of the circle...which is a disk $\endgroup$ – Triatticus May 3 '17 at 16:34
  • $\begingroup$ but why the region of bigger circle is equal to -2;0 ? and is equal x+2 ?? $\endgroup$ – Guldauren Bissenbayeva May 3 '17 at 16:49
  • $\begingroup$ The one with $-1$ refers to the circle on the right, the one with $+2$ refers to the left circle. The radius of the right circle is 1, the left circle has a radius of $\dfrac{1}{2}$. varsitytutors.com/hotmath/hotmath_help/topics/… $\endgroup$ – Triatticus May 3 '17 at 17:15

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