First slide

Functions (XII)

Question

The domain of $f (x) = \sin^{- 1} \{\log_{3} (\frac{x^{2}}{3})\}$ is

Moderate

A

$(- \infty, 3]$
B

$[3, \infty)$
C

$[- 3, - 1] \cup [1, 3]$
D

$(- 9, - 1) \cup (1, 9)$

Solution

$- 1 \leq \log_{3} (\frac{x^{2}}{3}) \leq 1 \Rightarrow 1 \leq x^{2} \leq 9 x^{2} - 1 \geq 0 \Rightarrow x \in (- \infty, 1] \cup [1, \infty) x^{2} - 9 \leq 0 \Rightarrow x \in [- 3, 3]$

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