Question

The domain of the function $f\left(x\right)=\sqrt{x-2}+\sqrt{5-x}$ is

• A. $(2,5)$
• B.
  $(-\infty ,2]\cup [5,\infty )$
• C. $[2,5]$
• D. $(2,\infty )$

Answer 1

The correct option is C $[2,5]$

For $f\left(x\right)$ to be defined,
$x-2\ge 0\text{and}5-x\ge 0$
$\Rightarrow x\ge 2\text{and}x\le 5$
$\Rightarrow x\in [2,5]$