First slide

Introduction to ITF

Question

Domain of $S i n^{- 1} {(\log_{2} (\frac{x^{2}}{2}))}^{}$ is

Moderate

A

$[- 2, - 1]$
B

$[1, 2]$
C

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

$[- 2, 0]$

Solution

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

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