Question

The solution of the inequality $\sqrt{x-2}\ge -1$ is

• A. $[2,3)$
• B. (2, 3)
• C. x > 2
• D. $x\ge 2$

Answer 1

The correct option is D $x\ge 2$

$x-2\ge 0\mathrm{for}\sqrt{x-2}\mathrm{to}\mathrm{get}\mathrm{defined}.\therefore x\ge 2\mathrm{Now}\sqrt{x-2}\ge -1\mathrm{is}\mathrm{always}\mathrm{true},\mathrm{as}\mathrm{square}\mathrm{roots}\mathrm{are}\mathrm{always}\mathrm{non}-\mathrm{negative}.\mathrm{Hence},x\ge 2.$