Question

The domain of the function $f(x)=\sqrt{{\log }_{0.5}x!}$ is

• A. $\{0,1,2,3,\dots \}$
• B. $\{1,2,3,\dots \}$
• C. $(0,\infty )$
• D. $\{0,1\}$

Answer 1

Answer: (D)

Given, $f(x)=\sqrt{{\log }_{0.5}x!}$
$f(x)$ is defined when
${\log }_{0.5}x!\ge 0$
$\Rightarrow x!\le (0.5{)}^0$
$\Rightarrow x!\le 1$
$\therefore x\in \{0,1\}$