Question

The set of values of $x$ for which inequality holds true
$\sqrt{x-2}\ge -1$ is

Answer 1

Given $\sqrt{x-2}\ge -1$

For expression to be defined
$x-2\ge 0\Rightarrow x\ge 2\cdots \left(1\right)$

Now,for given expression

$\sqrt{x-2}\ge -1\forall x\in [2,\infty )$
as square roots are always non-negative

Hence $x\ge 2$

Note: Some students solve it by squaring on both sides for which $x-2\ge 1$ or $x\ge 3$ clearly interval $[2,3)$ is lost.

Hence the correct answer is option C.