Answer:
Option c
[tex]y\leq -\sqrt{x} +1[/tex]
Step-by-step explanation:
To solve this type of problem the most efficient method is to select any point within the shaded region, for example, point (1,-1). Then introduce this point in the inequality:
[tex]y\leq -\sqrt{x} +1[/tex]
Then we have left:
[tex](-1)\leq -\sqrt{1} + 1[/tex]
Note that the inequality is satisfied. [tex]- \sqrt{1} +1 = 0[/tex] is greater than -1
Now we take the inequality shown in option c [tex]y\leq -\sqrt{x} +1[/tex] and substitute a point belonging to the curve [tex]y = -\sqrt {x} +1[/tex]
This point is (1, 0)
[tex](0) \leq -\sqrt{1} +1[/tex]
[tex](0) \leq 0[/tex]
Note that the inequality is satisfied. Therefore the correct option is the option c
