The domain of the function $f(x)=\sqrt{\log _{0.5} x !}$ is
The domain of the function $f(x)=\sqrt{\log _{0.5} x !}$ is
$\{0,1,2,3, \ldots\}$
$\{1,2,3, \ldots\}$
$(0, \infty)$
$\{0,1\}$
Solution
We have, $f(x)=\sqrt{\log _{0.5} x !}$
So, $f(x)$ will be defined when,
$\begin{aligned}
& \log _{0.5} x ! \geq 0 \\
& x ! \leq(0.5)^0 \\
& x ! \leq 1 \quad \therefore x \in\{0,1\}
\end{aligned}$
Hence, the domain of the function is $\{0,1\}$.