Question

The domain of the function $f\left(x\right)=\sqrt{\frac{x-8}{5-x}}$ is

• A. $(5,8]$
• B. $(13,\infty )$
• C. $[5,8)$
• D. $(5,\infty )$

Answer 1

The correct option is A $(5,8]$

Given,

$f\left(x\right)=\sqrt{\frac{x-8}{5-x}}$

The given function is defined for $(x-8)(5-x)\ge 0$ and $x\ne 5$
$\Rightarrow (x-8)(x-5)\le 0$
$\Rightarrow 5<x\le 8$
$\Rightarrow (5,8]$
Hence, option 'A' is correct.