Question

Domain of the function $f(x)=\log (\sqrt{x-4}+$ $\sqrt{6-x})$ is

• A. $[4,\infty ]$
• B. $(-\infty ,6)$
• C. [4, 6]
• D. None of these

Answer 1

Answer: (C)

$f(x)=\log (\sqrt{x-4}+\sqrt{6-x})$
$\sqrt{x-4}\ge 0,\sqrt{6-x}\ge 0$
$\Rightarrow$ $x-4\ge 0,6-x\ge 0$
$\Rightarrow$ $x\ge 4,x\le 6$
$\therefore$ Domain is [4, 6]