Question

The domain of $f\left(x\right)={\log }_2(\sqrt{x-5}+\sqrt{6-x})$ is

• A. $[5,6]$
• B. $(5,6)$
• C. $(-\infty ,5)$
• D. $(6,\infty )$

Answer 1

The correct option is A $[5,6]$

Given,

$f\left(x\right)={\log }_2(\sqrt{x-5}+\sqrt{6-x})$

For log to be defined

$\sqrt{x-5}+\sqrt{6-x}>0$
$5\le x$ & $x\le 6$
Combining the domains, we get
$5\le x\le 6$