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).
$l o g_{2} (2 y - x^{2} + 1) > l o g_{2} y, \sqrt{y - 2 x + 4} < \sqrt{8 - x}$

Open in App

Solution

R.E.F image
$l o g_{2} (2 y - x^{2} + 1) > l o g_{2} y,$ $\sqrt{y - 2 x + 4} < \sqrt{8 - x}$
base is $> 1$ Square both side
$2 y - x^{2} + 1 > y$ $y - 2 x + 4 < 8 - x$
$y > x^{2} - 1$ $y < x + 4$
Comparing both

Suggest Corrections

Similar questions

| x | + | y | < 4, l o g_{2} (2 y - x^{2} + 4) > l o g_{2} (y + 1)

y ⩾ \sqrt{1 - x^{2}}, y + | x | ⩽ 4

Join BYJU'S Learning Program