Question

Find the domain of $f\left(x\right)={\log }_{10}{\log }_2{\log }_{\pi /2}({\tan }^{-1}x{)}^{-1}$

Answer 1

We must have
${\log }_2{\log }_{\pi /2}(ta{n}^{-1}x{)}^{-1}>0$
or ${\log }_{\pi /2}(ta{n}^{-1}x{)}^{-1}>1$
or $0<(ta{n}^{-1}x{)}^{-1}<\frac{2}{\pi }$
or $\frac{\pi }{2}<ta{n}^{-1}x<\infty$, which is not possible. Hence the domain is $\varphi$