Question

select the correct answer.
what is the range of function g?
$g(x) = \sqrt{x - 1} + 2$
a. $y \leq 1$
b. $y \geq 2$
c. $y \geq 1$
d. $y \leq 2$

Explanation:

Step1: Analyze square root domain/range

The square root function $\sqrt{x-1}$ has a minimum value of $0$ (since square roots of real numbers are non-negative, i.e., $\sqrt{x-1} \geq 0$ for all valid $x$ where $x-1 \geq 0$).

Step2: Add constant to find function range

Add 2 to both sides of the inequality for the square root:
$\sqrt{x-1} + 2 \geq 0 + 2$
Simplify to get $g(x) \geq 2$, or $y \geq 2$.

Answer:

B. $y \geq 2$