First slide

Introduction to ITF

Question

The domain of $\sin^{- 1} [\log_{2} (x^{2} / 2)]$ is

Moderate

A

$[- 2, - 1]$
B

$[1, 2]$
C

$[- 2, - 1] \cup [1, 2]$
D

$[- 2, 0]$

Solution

$W e k n o w t h a t d o m a i n o f \sin^{- 1} x i s [- 1, 1] . ∴ \sin^{- 1} [\log_{2} (\frac{x^{2}}{2})] i s d e f i n e d i f - 1 \leq \log_{2} (\frac{x^{2}}{2}) \leq 1 \Rightarrow 2^{- 1} \leq \frac{x^{2}}{2} \leq 2 \Rightarrow 1 \leq x^{2} \leq 4 \Rightarrow x \in [- 2, - 1] \cup [1, 2]$

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