Question

Domain of $f(x)=\sqrt{\log (2x-x^2)}$ is

• A. $(0,\infty )$
• B. $(1,\infty )$
• C. $(0,1)\cup (1,\infty )$
• D. none of these

Answer 1

Answer: (D)

$f(x)$ will be real if $\log (2x-x^2)\ge 0$
$\Rightarrow 2x-x^2\ge e^{\circ }=1$
$\Rightarrow x^2-2x+1\le 0$
$\Rightarrow (x-1{)}^2\le 0$
$\Rightarrow (x-1{)}^2=0$
$\Rightarrow x=1$
$\therefore D_f=\left\{1\right\}$.