Browse Questions

# The domain of $sin^{-1}\big[log_3(\large\frac{x}{3})\big]$ is

(A) $[1,9]$ (B) $[-11,9]$ (C) $[-9,1]$ (D) $[-9,-1]$

Toolbox:
• $log\frac{a}{b}=loga-l$ogb
• $log_b\large a=\frac{loga}{logb}$ (with any base)
• $log_a\large a=1$
• Domain of $sin^{-1}x=[-1,1]$
• $log1=0$
• $log(x^n)=nlogx$
Ans: (A) [1,9]
Domain of $sin^{-1}x=[-1,1]$
$\Rightarrow\:-1\leq\:log_3(\frac{x}{3})\leq 1$
$\Rightarrow\:-1\leq (log_3\large x$-$log_3\large3)\leq 1$
$\Rightarrow\:-1\leq (log_3\large x$-1)$\leq1$
$\Rightarrow\:0\leq (log_3\large x$)$\leq2$