1.Relation and Function
easy

The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is

A

$[1, 4]$

B

$[-4, 1]$

C

$[-1, 4]$

D

None of these

Solution

(a) $f(x) = {\sin ^{ – 1}}[{\log _2}(x/2)]$, Domain of ${\sin ^{ – 1}}x$ is $x \in [ – 1,\,1]$ 

==> $ – 1 \le {\log _2}(x/2) \le 1$ ==> $\frac{1}{2} \le \frac{x}{2} \le 2$

==> $1 \le x \le 4$

$\therefore$  $x \in [1,\,4]$.

Standard 12
Mathematics

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