First slide

Functions (XII)

Question

The domain of the function
$f (x) = \sin^{- 1} (\log_{3} \frac{x}{3})$ is

Moderate

A

$[- 1, 9]$
B

$[1, 9]$
C

$[- 9, 1]$
D

$[3, 9]$

Solution

The function f is defined only if $- 1 \leq \log_{3} (x / 3) \leq 1$ This inequality is possible only if
$1 / 3 \leq x / 3 \leq 3 i.e., 1 \leq x \leq 9$

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