Question

$f\left(x\right)=\log (\sqrt{x-4}+\sqrt{6-x})$ is defined for

• A. $\left[6,8\right]$
• B. $\left[2,4\right]$
• C. $\left[4,6\right]$
• D. None of these

Answer 1

The correct option is C

$\left[4,6\right]$

Explanation for the correct option:

Find the domain of the given function:

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

For given function to be defined,

$x-4\ge 0$ and $6-x\ge 0$

$\Rightarrow$$x\ge 4$ and $x\le 6$

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

Hence, Option ‘C’ is Correct.