Question

Solve: $\sqrt{x-2}$ ≥ -1

• A. [2,3)
• B. [3,$\infty$)
• C. [2,$\infty$)
• D. ($-\infty$,3]

Answer 1

The correct option is C

[2,$\infty$)

We must have x-2 ≥ 0 for $\sqrt{x-2}$ to get defined, so, x ≥ 2

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

Hence x ≥ 2

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