Question

On the coordinates plane XOY hatch a set of points whose coordinates satisfy the following inequalities in two variables x and y (show the boundary belonging to the set by a solid line and that not belonging to the set by a dash line).
$|x|+|y|<4,lo{g}_2(2y-x^2+4)>lo{g}_2(y+1)$

Answer 1

R.E.F image

$|x|+|y|<4$ $lo{g}_2(2y-x^2+4)>lo{g}_2(y+1)$

case 1, $x>0,y>0$ base of log is $>1$

$x+y<4$ $\because 2y-x^2+4>y+1$

case - 2 $y>x^2-3$

$x>0,y<0$

$x-y<4$

case - 3

$x<0,y>0$

$x-y<4$

case - 4

$x<0,y<0$

$x+y>-4$

Comparing both