Question

The domain of the function, $f\left(x\right)={\log }_{10}(\sqrt{x-4}+\sqrt{6-x})$ is

• A. $(4,6)$
• B. $[4,6]$
• C. $[4,6)$
• D. none of these

Answer 1

The correct option is B $[4,6]$

Given,

$f\left(x\right)={\log }_{10}(\sqrt{x-4}+\sqrt{6-x})$

For given function to be defined,
$\Rightarrow x-4\ge 0$ and $6-x\ge 0\Rightarrow x\ge 4$and $x\le 6$

$\therefore$ Domain of $\left(x\right)=[4,6]$