Question

The domain of $f\left(x\right)=\sqrt{x-2}+\frac{1}{\log (5-x)}$ if

• A. $[2,\infty )$
• B. $[2,5]$
• C. $[2,4)\cup (4,5)$
• D. $(-\infty ,\infty )$

Answer 1

The correct option is C $[2,4)\cup (4,5)$

$x-2⩾0$ $\Rightarrow x⩾2$
$5-x>0$ & $5-x\ne 1$
$x<5$ $x\ne 4$
$\Rightarrow x\in [2,5)-\left\{4\right\}$
$[2,4)\cup (4,5)$