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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