Question

The domain of the functions $f\left(x\right)=\sqrt{\log (2x-x^2)}$ is

• A. $(0,2)$
• B. $[0,2]$
• C. $\left\{1\right\}$
• D. none

Answer 1

Answer: (D)

none

$2x-x^2>0$

$x^2-2x<0$

$x(x-2)<0$

$x\in (0,2)$

also, $\log (2x-x^2)\ge 0$

$2x-x^2\ge 1$

$x^2-2x+1\le 0$

$(x-1{)}^2\le 0$

$x\le 1$

$x6(0,1]$