Question

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{x-2}}+\frac{1}{\sqrt{5-x}}$ is

• A. $[2,5]$
• B. $(2,5)$
• C. $[2,5)$
• D. $(2,5]$

Answer 1

The correct option is B $(2,5)$

Given,

$f\left(x\right)=\frac{1}{\sqrt{x-2}}+\frac{1}{\sqrt{5-x}}$

For the $f\left(x\right)$ to be defined.
$x-2>0\Rightarrow x>2$
$5-x>0\Rightarrow x<5$
$\Rightarrow x\in (2,5)$