First slide

Functions (XII)

Question

The domain of sin^-1 $[\log_{3} (\frac{x}{3})]$ is

Moderate

A

1.[1,9]
B

2.[-1,9]
C

3.[-9,1]
D

4.[-9,-1]

Solution

Let f(x)=sin^-1 $[\log_{3} (\frac{x}{3})]$
since Domain of sin^-1x is [-1,1]
$∴ - 1 \leq [\log_{3} (\frac{x}{3})] \leq 1 \Rightarrow 3^{- 1} \leq \frac{x}{3} \leq 3 \Rightarrow 1 \leq x \leq 9$
Hence domain of in^-1 $[\log (\frac{x}{3})]$ is [1,9]

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